Search

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates quantum electrodynamics. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism. [ABSTRACT FROM AUTHOR]

We consider the ground state and the ground state energy of an atom with spinless electrons in the framework of non-relativistic quantum electrodynamics. We show that the ground state energy as well as the ground state depend analytically on the parameters of the group of dilations, the parameter of a group of spatial dependent phase changes, and on the minimal coupling constant. As a corollary we obtain spatial exponential decay of the ground state as well as of its dilation analytic extension. No infrared regularization is needed for the result. Our result is based on operator theoretic renormalization. [ABSTRACT FROM AUTHOR]

Two-dimensional Weyl–Dirac relativistic fermions have attracted tremendous interest in condensed matter as they mimic relativistic high-energy physics. This paper concerns two-dimensional Weyl–Dirac operators in the presence of magnetic fields, in addition to a short-range scalar electric potential of the Bessel–Macdonald-type, restricted to its positive spectral subspace. This operator emerges from the action of a pristine graphene-like QED3 model recently proposed by De Lima, Del Cima, and Miranda, "On the electron–polaron–electron–polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics," Eur. Phys. J. B93, 187 (2020). A magnetic Lieb–Thirring-type inequality à la Shen is derived for the sum of the negative eigenvalues of the magnetic Weyl–Dirac operators restricted to their positive spectral subspace. An application to the stability of bipolarons in graphene in the presence of magnetic fields is given. [ABSTRACT FROM AUTHOR]

We report on a result on quantum electrodynamics on a three-dimensional Euclidean spacetime. The model is formulated on a toroidal lattice with unit volume and variable lattice spacing. The result is that the renormalized partition function is bounded above and below uniformly in the lattice spacing. This is a first step toward showing that the partition function and correlation functions have limits as the lattice spacing goes to zero. [ABSTRACT FROM AUTHOR]

We continue the study of the ultraviolet problem for quantum electrodynamics in d = 3. The model is defined on a fine toroidal lattice, and we seek control as the lattice spacing goes to zero. The problem is analyzed using Balaban's formulation of the renormalization group. This involves a sequence of transformations consisting of a split into large and small field regions, then block averaging, and then scaling. The effective actions generated by this method depend strongly on certain multi-scale propagators and minimizers. The study of these objects both for fermions and for gauge fields is the content of this paper. Earlier work on the subject is reviewed. In addition for fermions, a polymer expansion is obtained for the determinants of the fermion propagators. For the gauge field, a detailed local regularity result is obtained for the minimizers. [ABSTRACT FROM AUTHOR]

Dirac, Fock, and Podolsky devised a relativistic model in 1932 in which a fixed number of N Dirac electrons interact through a second-quantized electromagnetic field. It is formulated with the help of a multitime wave function ψ ( t 1 , x 1 , ... , t N , x N ) that generalizes the Schrödinger multiparticle wave function to allow for a manifestly relativistic formulation of wave mechanics. The dynamics is given in terms of N evolution equations that have to be solved simultaneously. Integrability imposes a rather strict constraint on the possible forms of interaction between the N particles and makes the rigorous construction of interacting dynamics a long-standing problem, also present in the modern formulation of quantum field theory. For a simplified version of the multitime model, in our case describing N Dirac electrons that interact through a relativistic scalar field, we prove well-posedness of the corresponding multitime initial value problem and discuss the mechanism and type of interaction between the charges. For the sake of mathematical rigor, we are forced to employ an ultraviolet cutoff in the scalar field. Although this again breaks the desired relativistic invariance, this violation occurs only on the arbitrarily small but finite length-scale of this cutoff. In view of recent progress in this field, the main mathematical challenges faced in this work are, on the one hand, the unboundedness from below of the free Dirac Hamiltonians and the unbounded, time-dependent interaction terms, and on the other hand, the necessity of pointwise control of the multitime wave function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is a self-adjoint operator on a boson-fermion Fock space. It is shown that under spatially localized conditions and momentum regularity conditions, the total Hamiltonian has a ground state for all values of coupling constants. In particular, its multiplicity is finite. [ABSTRACT FROM AUTHOR]

We investigate the controllability of the Jaynes-Cummings dynamics in the resonant and nearly resonant regime. We analyze two different types of control operators acting on the bosonic part, corresponding—in the application to cavity Quantum Electro Dynamics—to an external electric and magnetic field, respectively. For these models, we prove approximate controllability for all values of the coupling constant g ∈ R , except those in a countable set S* which is explicitly characterized in the statement. The proof relies on a spectral analysis which yields the non-resonance of the spectrum for every g ∈ R \ S * . [ABSTRACT FROM AUTHOR]

An analogy with real Clifford algebras on even-dimensional vector spaces suggests assigning an ordered pair (s, t) of space and time dimensions (or equivalently an ordered pair (m, n) of metric and KO dimensions) modulo 8 to any algebraic structure (that we call CPT corepresentation) represented over a Hilbert space by two self-adjoint involutions and an anti-unitary operator having specific commutation relations. It is shown that this assignment is compatible with the tensor product: the space and time dimensions of the tensor product of two CPT corepresentations are the sums of the space and time dimensions of its factors, and the same holds for the metric and KO dimensions. This could provide an interpretation of the presence of such algebras in PT-symmetric Hamiltonians or the description of topological matter. This construction is used to build an indefinite (i.e., pseudo-Riemannian) version of the spectral triple of noncommutative geometry, defined over a Krein space and classified by the pair (m, n) instead of the KO dimension only. Within this framework, we can express the Lagrangian (both bosonic and fermionic) of a Lorentzian almost-commutative spectral triple. We exhibit a space of physical states that solves the fermion-doubling problem. The example of quantum electrodynamics is described. [ABSTRACT FROM AUTHOR]

We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let H(Λ, V) denote the Hamiltonian of QED1+3 on the three-dimensional torus of volume V and with ultraviolet cutoff Λ. Then there exists a constant 0 < μ(Λ, V) < ∞ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: H r e n ( Λ , V ) ≡ H Λ , V + μ Λ , V ⋅ 1 ≥ 0. [ABSTRACT FROM AUTHOR]

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect.We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t α Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α = 1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α ≥ 1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods. [ABSTRACT FROM AUTHOR]

In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states. [ABSTRACT FROM AUTHOR]

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann--Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs. [ABSTRACT FROM AUTHOR]

In recent work, we formulated a new set of electrodynamic equations for massive dyons using dual octonion algebra. Starting with the dual octonion algebra, we develop the generalized electromagnetic field equations for massive dyons. We have made an attempt to obtain the symmetrical form of generalized Proca-Dirac- Maxwell equations with respect to the dual octonion form. Furthermore, we have constructed the Klein-Gordon field equation for massive dyons in terms of the dual octonion. Thus the main advantages of present formalism are discussed in terms of compact and simpler notations of dual octonion components of massive dyons despite of non-associativity of dual octonions. [ABSTRACT FROM AUTHOR]

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1/2 + Z+, we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons. [ABSTRACT FROM AUTHOR]

For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban's approach to the renormalization group. [ABSTRACT FROM AUTHOR]

We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of a no-pair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential. We prove that the infimum of the spectrum of the no-pair operator is an evenly degenerate eigenvalue. In particular, we show that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the fine-structure constant and the ultraviolet cut-off and for all Coulomb coupling constants less than the critical one of the Brown-Ravenhall model, 2/(2/π + π/2). For Coulomb coupling constants larger than the critical one, we show that the quadratic form of the no-pair operator is unbounded below. Along the way we discuss the domains and operator cores of the semi-relativistic Pauli-Fierz and no-pair operators, for Coulomb coupling constants less than or equal to the critical ones. [ABSTRACT FROM AUTHOR]

Supersymmetric QED hydrogen-like bound states are remarkably similar to nonsupersymmetric hydrogen, including an accidental degeneracy of the fine structure and is broken by the Lamb shift. This article classifies the states, calculates the leading order spectrum, and illustrates the results in several limits. The relation to other nonrelativistic bound states is explored. [ABSTRACT FROM AUTHOR]

The Pauli-Fierz model H(α) in nonrelativistic quantum electrodynamics is considered. The external potential V is sufficiently shallow and the dipole approximation is assumed. It is proven that there exist constants 0 < α- < α+ such that H(α) has no ground state for |α| < α-, which complements an earlier result stating that there is a ground state for |α| > α+. We develop a suitable extension of the Birman-Schwinger argument. Moreover, for any given δ > 0 examples of potentials V are provided such that α+ - α- < δ. [ABSTRACT FROM AUTHOR]

For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum. [ABSTRACT FROM AUTHOR]

In this paper, the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. A scaled total Hamiltonian is introduced and its asymptotic behavior is investigated. In the main theorem, it is shown that the scaled total Hamiltonian converges to a self-adjoint operator in the strong resolvent sense, and the effective potential of the Dirac field is derived. [ABSTRACT FROM AUTHOR]

We wish to study an application of Stueckelberg's relativistic quantum theory in the framework of general relativity. We study the form of the wave equation of a massive body in the presence of a Schwarzschild gravitational field. We treat the mathematical behavior of the wavefunction also around and beyond the horizon (r = 2M). Classically, within the horizon, the time component of the metric becomes spacelike and distance from the origin singularity becomes timelike, suggesting an inevitable propagation of all matter within the horizon to a total collapse at r = 0. However, the quantum description of the wavefunction provides a different understanding of the behavior of matter within the horizon. We find that a test particle can almost never be found at the origin and is more probable to be found at the horizon. Matter outside the horizon has a very small wavelength and therefore interference effects can be found only on a very small atomic scale. However, within the horizon, matter becomes totally 'tachyonic' and is potentially 'spread' over all space. Small location uncertainties on the atomic scale become large around the horizon, and different mass components of the wavefunction can therefore interfere on a stellar scale. This interference phenomenon, where the probability of finding matter decreases as a function of the distance from the horizon, appears as an effective gravitational repulsion. [ABSTRACT FROM AUTHOR]

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a G-parity transformation, respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite, respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions. [ABSTRACT FROM AUTHOR]

We construct the time-evolution for the second-quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom involved. Earlier works on this (e.g., Ruijsenaars) observed the Shale-Stinespring condition and showed that the one-particle time-evolution can be lifted to Fock space if and only if the external field had zero magnetic components. We scrutinize the idea, observed earlier by Fierz and Scharf, that the time-evolution can be implemented between time varying Fock spaces. In order to define these Fock spaces we are led to consider classes of reference vacua and polarizations. We show that this implementation is up to a phase independent of the chosen reference vacuum or polarization and that all induced transition probabilities are well-defined and unique. [ABSTRACT FROM AUTHOR]

Controlling the time evolution of the population of two states in cavity quantum electrodynamics is necessary by tuning the modified Rabi frequency in which the extra classical effect of electromagnetic field is taken into account. The theoretical explanation underlying the perturbation of potential on spatial regime of bloch sphere is by the use of Bagrov–Baldiotti–Gitman–Shamshutdinova–Darboux transformations [Bagrov et al., “Darboux transformation for two-level system,” Ann. Phys. 14, 390 (2005)] on the electromagnetic field potential in one-dimensional stationary Dirac model in which the Pauli matrices are the central parameters for controlling the collapse and revival of the Rabi oscillations. It is shown that by choosing σ1 in the transformation generates the parabolic potential causing the total collapse of oscillations, while {σ2,σ3} yield the harmonic oscillator potentials ensuring the coherence of qubits. [ABSTRACT FROM AUTHOR]

A theoretical prediction for the total width of the positronium decay in quantum electrodynamics has been given by Kniehl et al. [“Irrational constants in positronium decays,” Nucl. Phys. B (Proc. Suppl.) 184, 14 (2008), arXiv:hep-ph/0811.0306] in the form of an expansion in Sommerfeld’s fine-structure constant. The coefficients of this expansion are given in the form of two-dimensional definite integrals, with an integrand involving the polylogarithm function. We provide here an analytic expression for the one-loop contribution to this problem. [ABSTRACT FROM AUTHOR]

The retarded van der Waals potential, as first obtained by Casimir and Polder, is usually computed on the basis of nonrelativistic quantum electrodynamics . The Hamiltonian describes two infinitely heavy nuclei, charge e, separated by a distance R and two spinless electrons, charge -e, nonrelativistically coupled to the quantized radiation field. Casimir and Polder used the dipole approximation and small coupling to the Maxwell field. We employ here the full Hamiltonian and determine the asymptotic strength of the leading -R-7 potential, which is valid for all e. Our computation is based on a path integral representation and expands in 1/R, rather than in e. [ABSTRACT FROM AUTHOR]

In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The spectral scattering theory is studied as well and it is shown that asymptotic fields exist and the spectral gap is closed. [ABSTRACT FROM AUTHOR]

We study the infrared problem in the usual model of quantum electrodynamics with nonrelativistic matter. We prove spectral and regularity properties characterizing the mass shell of an electron and one-electron infraparticle states of this model. Our results are crucial for the construction of infraparticle scattering states, which are treated in a separate paper. [ABSTRACT FROM AUTHOR]

We show the existence of all the 36 eightfold way mesons and determine their masses and dispersion curves exactly, from dynamical first principles such as directly from the quark-fluon dynamics. We also give a proof of confinement below the two-meson energy threshold. For this purpose, we consider an imaginary time functional integral representation of a 3+1 dimensional lattice QCD model with Wilson action... [ABSTRACT FROM AUTHOR]

The character expansion method was introduced by Balantekin [Phys. Rev. D 62, 085017 (2000)] for integration over the unitary group and, in particular, for calculating the well-known Harish–Chandra–Itzykson–Zuber integral where the coefficient matrices in the integrand are square matrices with nonzero determinants. However, in some applications such as the capacity analysis of multiple-input multiple-output channels in wireless communications and information theory, or applying the color-flavor transformation to lattice quantum chromodynamics in physics, or the theory of random matrices in mathematics, the integration over the unitary group is required where general rectangular complex matrices appear in the integrand. In this paper, we use the character expansion of groups to generalize two integrals over the unitary group that have general rectangular complex matrices in the integrand. Although we consider only two integrals, we believe that the integration framework presented here can be used for other integrals over unitary matrices. [ABSTRACT FROM AUTHOR]

We obtain from first principles, i.e., from the quark-gluon dynamics, the Gell’Mann-Ne’eman baryonic eightfold way energy momentum spectrum exactly in an imaginary-time functional integral formulation of strongly coupled lattice quantum chromodynamics in 3+1 dimensions, with local SU(3)c gauge and global SU(3)f flavor symmetries. We take the hopping parameter κ and the pure gauge coupling β satisfying the strong coupling regime condition 0<β«κ«1. The form of the 56 baryon fields emerges naturally from the dynamics and is unveiled using the hyperplane decoupling method. There is no a priori guesswork. In the associated physical quantum mechanical Hilbert space H, spectral representations are derived for the two-baryon functions, which are used to rigorously detect the particles in the energy-momentum spectrum. Using the SU(3)f symmetry, the 56 baryon states admit a decomposition into 8×2 states associated with a spin 1/2 octet and 10×4 states associated with a spin 3/2 decuplet. The states are labeled by the quantum numbers of total hypercharge Y, total isospin I, its third component I3, and the value of the quadratic Casimir of SU(3)f; they also carry a label of total spin J and its z component Jz. The total spin operators are defined using π/2 rotations about the spatial coordinate axes and for improper zero momentum baryon states agree with the infinitesimal generators of the continuum. We show there is a partial restoration of continuous rotational symmetry which implies that all the octet (decuplet) masses are the same. For β=0, the masses of the 56 baryon states have the form M=-3 ln κ-3κ3/4+κ6r(κ), with r(κ) analytic. There is no mass splitting within the octet (decuplet). However, we find an octet-decuplet mass splitting given by 3κ6/4+O(κ7). For β=0, [M(κ,β)-(-3 lnκ)], the non-singular part of the masses, is analytic in κ and β and the mass splitting persists for β≠0. For spatial momentum p≠0, p≠(p1,p2,p3)∈(−π,π]3, the 56 baryon dispersion curves have the form w(κ,p)=−3 ln κ-3κ3/4+κ3∑j=1,2,3(1-cos pj)/4+r(κ,p), where r(κ,p) is of O(κ6). For the octet, r(κ,p) is jointly analytic in κ and in each pj for small |Im pj|. For each baryon, there is an antibaryon related to it by charge conjugation and with identical spectral properties. It is shown that the spectrum associated with baryons and antibaryons is the only spectrum in the subspace of H with an odd number of quarks, up to near the meson-baryon energy threshold of ≈-5 ln κ. A new time reflection is found which is used to define a local spin flip symmetry. The spin flip symmetry, together with the usual parity, time reversal, and spatial π/2 rotation symmetries and analytic implicit function arguments, are used to obtain these results. Our method extends to the SU(N)f case to uncover (2N+2)!/[3!(2N-1)!] baryon states and also to treat mesons. Coupling our baryon results with our similar results for the eightfold mesons (of asymptotic mass -2 lnκ) shows that the model exhibits confinement up to near the two-meson threshold. [ABSTRACT FROM AUTHOR]

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra su(2). The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard a† and a. The new operators also give rise to a natural family of two-oscillator couplings. These nonlinear couplings are not generally self-adjoint, but their low-energy limits are self-adjoint, exactly solvable, and stable. We discuss the structure of a theory involving these couplings. Such a theory might have as its ultra-low-energy limit a Lorentz-violating Abelian gauge theory, and we discuss the extremely strong astrophysical constraints on such a model. [ABSTRACT FROM AUTHOR]

We consider a model of quantum electrodynamics (QED) on a graph as the generalization of dimensional deconstruction with the Abelian symmetry. Arbitrary structures of the theory space correspond to the graphs consisting of vertices and edges. The mass spectrum of the model is expressed in terms of eigenvalues of the Laplacian for the graph. We also find that physical massless scalar modes are associated with the fundamental tie set matrix on the graph. We further investigate the one-loop divergences in the model by use of the background field method. [ABSTRACT FROM AUTHOR]

We consider the polaron model in the relativistic quantum electrodynamics. We prove that the ground state energy of the model is finite for all values of the fine-structure constant and the ultraviolet cutoff Λ. Moreover we give an upper bound and a lower bound of the ground state energy. [ABSTRACT FROM AUTHOR]

Superselection and constraints occur together in many gauge theories, and here we begin a study of such systems. Our main focus will be to analyze compatibility questions between constraining and superselection, and we will develop an example modelled on QED in which our framework is realized. We proceed from a generalization of Doplicher-Roberts superselection theory to the case of the nontrivial center, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorization of superselection structures. [ABSTRACT FROM AUTHOR]

In nonrelativistic quantum electrodynamics the charge of an electron equals its bare value, whereas the self-energy and the mass must he renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine structure constant α, in the case of a single, spinless electron. As is well known, if m denotes the bare mass and meff the mass computed from the theory, to order α one has meff/m= 1 +(8α/3π)log(1 +½(Λ/m))+O(α²) which suggests that meff/m = (Λ /m)8α.3π for small α. If correct, in order α² the leading term should be ½((8α/3π)log(Λ/m))². To check this point we expand meff/m to order α². The result is √Λ/m as leading term, suggesting a more complicated dependence of meff on m. [ABSTRACT FROM AUTHOR]

We consider a reformulation of quantum electrodynamics in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M matrix in lowest order. Solutions of the two-body equations are presented for muoniumlike systems for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed. [ABSTRACT FROM AUTHOR]

We study quantum chromodynamics (QCD) on a finite lattice Λ in the Hamiltonian approach. First, we present the field algebra AΛ as comprising a gluonic part, with basic building block being the crossed product C*-algebra C(G)xαG, and a fermionic (CAR-algebra) part generated by the quark fields. By classical arguments, AΛ has a unique (up to unitary equivalence) irreducible representation. Next, the algebra OΛi of internal observables is defined as the algebra of gauge invariant fields, satisfying the Gauss law. In order to take into account correlations of field degrees of freedom inside Λ with the “rest of the world,” we must extend OΛi by tensorizing with the algebra of external gauge invariant operators. This way we construct the full observable algebra OΛ. It is proved that its irreducible representations are labelled by Z3-valued boundary flux distributions. Then, it is shown that there exist unitary operators (charge carrying fields), which intertwine between irreducible sectors leading to a classification of irreducible representations in terms of the Z3-valued global boundary flux. By the global Gauss law, these three inequivalent charge superselection sectors can be labeled in terms of the global color charge (triality) carried by quark fields. Finally, OΛ is discussed in terms of generators and relations. [ABSTRACT FROM AUTHOR]

We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of compound particles). In this approximation the compound and elementary particles are considered on an equal basis. This means that creation and annihilation operators of compound particles can be introduced. The Hamiltonians, which specify the interactions between compound and elementary particles and between compound particles themselves, are found in terms of the interaction amplitudes for elementary particles. The nonrelativistic quantum electrodynamics is developed for systems containing both elementary and compound particles. Some applications of this theory are considered. [ABSTRACT FROM AUTHOR]

The convergence of integrals over charge densities is discussed in relation with the problem of electric charge and (nonlocal) charged states in quantum electrodynamics. Delicate points like the domain dependence of local charges as quadratic forms and the class of time smearing ensuring strong convergence of integrals of charge densities are analyzed and shown to be crucial in QED, also for the control of vacuum polarization effects leading to time dependence of the charge (Swieca phenomenon). The possibility of constructing physical charged states in the Feynman–Gupta–Bleuler gauge as limits of local state vectors is discussed, compatibly with the vanishing of the Gauss charge on local states. A modification of the Dirac exponential factor which yields the physical Coulomb fields from the Feynman–Gupta–Bleuler fields is shown to remove the infrared divergence of scalar products of local and physical charged states, allowing for a construction of physical charged fields with well-defined correlation functions with local fields. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The conflict between Gauss’ law constraint and the existence of the propagator of the gauge fields, at the basis of contradictory proposals in the literature, is shown to lead to only two alternatives, both with peculiar features with respect to standard quantum field theory. In the positive (interacting) case, the Gauss’ law holds in operator form, but only the correlations of exponentials of gauge fields exist (nonregularity) and the space translations are not strongly continuous, so that their generators do not exist. Alternatively, a Källen–Lehmann representation of the two point function of A[sub i] satisfying locality and invariance under space–time translations, rotations and parity is derived in terms of the two point function of F[sub μν]; positivity is violated, the Gauss’ law does not hold, the energy spectrum is positive, but the relativistic spectral condition does not hold. In the free case, θ-vacua exist on the observable fields, but they do not have time translationally invariant extensions to the gauge fields; the vacuum is faithful on the longitudinal field algebra and defines a modular structure (even if the energy is positive). Functional integral representations are derived in both cases, with the alternative between ergodic measures on real random fields or complex Gaussian random fields.© 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We consider a Pauli–Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum P=0. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An analysis of spinor redefinitions in the context of the Lorentz-violating quantum electrodynamics (QED) extension is performed. Certain parameters that apparently violate Lorentz invariance are found to be physically irrelevant as they can be removed from the Lagrangian using an appropriate redefinition of the spinor field components. It is shown that conserved currents may be defined using a modified action of the complex extension of the Lorentz group on the redefined spinors. This implies a natural correspondence between the apparently Lorentz-violating theory and conventional QED. Redefinitions involving derivatives are shown to relate certain terms in the QED extension to Lagrangians involving nonlocal interactions or skewed coordinate systems. The redundant parameters in the QED extension are identified and the Lagrangian is rewritten in terms of physically relevant coupling constants. The resulting Lagrangian contains only physically relevant parameters and transforms conventionally under Lorentz transformations. [ABSTRACT FROM AUTHOR]

Scaling limits of the Hamiltonian H of a system of N charged particles coupled to a quantized radiation field are considered. Ultraviolet cutoffs, ...[sub 1],…,...[sub N], are imposed on the radiation field and the Coulomb gauge is taken. It is the so-called Pauli-Fierz model in nonrelativistic quantum electrodynamics. We mainly consider two cases: (i) all the ultraviolet cutoffs are identical, ...[sub 1] = … = ...[sub N], (ii) supports of ultraviolet cutoffs have no intersection, supp ...[sub i]∩supp...=Ø, i &ne j. The Hamiltonian acts on L²(R[sup dN])⊗F, where F is a symmetric Fock space, and has the form H=H[sub e1]⊗1 + B + 1 ⊗ H[sub quad]. Here H[sub el] denotes a particle Hamiltonian, H[sub quad] a quadratic field operator, and B an interaction term. The scaling is introduced as H(κ)=H[sub el]⊗1+ κ[sup l]B+κ²1⊗H[sub quad], where κ is a scaling parameter and l ≤ 2 a parameter of the scaling. Performing a mass renormalization we consider the scaling limit of H(κ) as κ→∞ in the strong resolvent sense. Then effective Hamiltonians H[sub eff] in L²(R[sup dN]) infected with reaction of effect of the radiation field is derived. In particular (1) effective Hamiltonians with an effective potential for l = 2, and (2) effective Hamiltonians with an observed mass for l= 1, are obtained. [ABSTRACT FROM AUTHOR]

Examines the derivative expansion of the one-loop effective action in quantum electrodynamics. Coefficient functions which appear in purely electric and magnetic cases; Expansion of the derivative terms in powers of the proper time; Use of a special matrix basis in order to deal with functions of antisymmetric tensors.

Investigates the canonical quantization of Chern-Simons quantum electrodynamics as an indefinite metric quantum field theory in the covariant gauges. Construction of the path space formulas for indefinite metric; Representation of the gauge field in Hilbert space; Derivation of the operators for the gauge fields and their conjugate momenta.

Examines the deformation of massless Gupta-Bleuler triplets in 3+2 De Sitter space massless field. Occurrence of identity representation in Gupta-Bleuler triplets of electrodynamics; Presence of massless Golstone fields; Description of the 3+2 De Sitter massless field.