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We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to acquire "which path" information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. We provide estimates of the decoherence time for such quantum superpositions. We believe that the fact that a black hole will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes in a quantum theory of gravity. [ABSTRACT FROM AUTHOR]

• We study the many-body t-matrix approximation for the weakly interacting bose gas. • We solved the coupled equation for the t-matrix and the condensate density. • This results lead to the correct order of the phase transition. We have proved in the many-body t-matrix approximation for the weakly interacting Bose gas the infrared divergences are exactly removed. We also show that this t-matrix becomes very temperature-dependent and, as the temperature approaches to T c it vanishes at the transition point. This leads to a smooth change of condensate density and compressibility at T c , implying the second order phase transition occurs at T c. [ABSTRACT FROM AUTHOR]

In this note we critically re-examine the usual procedure of quantization of classical wave equations with static sources. We point out that the origin of infrared difficulties in the so called van Hove model is related to the complex Hilbert space structure one puts on the classical phase space and the corresponding unitarization of the classical symplectic evolution. Whereas in the usual framework the condition of infrared regularity forces the total charge of the external source to vanish, in our setting the infrared regularity condition is equivalent to having a source with a finite (electrostatic) energy. A similar analysis could be applied to models of field-particle interaction such as the Nelson model.

Within the standard V − A theory of weak interactions, Quantum Electrodynamics (QED) and the linear σ -model (L σ M) of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron β − -decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order O (α / π) , induced by hadronic structure of the nucleon, to the rate of the neutron β − -decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin's analysis of contributions of strong low-energy interactions (Phys. Rev.164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative β − -decay and neutron β − -decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective V − A vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and L σ M , which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the L σ M , where the effective V − A vertex of hadron–lepton current–current interactions is caused by the W − -electroweak-boson exchange. [ABSTRACT FROM AUTHOR]

Stueckelberg QED with massive photon is known to be renormalizable. But the limit of the mass going to zero is interesting because it brings the resolution to infrared questions through the role of Stueckelberg field at null infinity in addition to providing new asymptotic symmetries. Such symmetries facilitate the soft photon theorems also. [ABSTRACT FROM AUTHOR]

A space-periodic ground state is shown to exist for lattices of point ions in R coupled to the Schrödinger and scalar fields. The coupling requires renormalization due to the singularity of the Coulomb self-action. The ground state is constructed by minimizing the renormalized energy per cell. This energy is bounded from below when the charge of each ion is positive. The elementary cell is necessarily neutral. [ABSTRACT FROM AUTHOR]

Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary. [ABSTRACT FROM AUTHOR]

A space-periodic ground state is shown to exist for lattices of smeared ions in ℝ³ coupled to the Schrödinger and scalar fields. The elementary cell is necessarily neutral. The one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) lattices in ℝ³ are considered, and a ground state is constructed by minimizing the energy per cell. The case of a 3D lattice is rather standard, because the elementary cell is compact, and the spectrum of the Laplacian is discrete. In the cases of 1D and 2D lattices, the energy functional is differentiable only on a dense set of variations, due to the presence of the continuous spectrum of the Laplacian that causes the infrared divergence of the Coulomb bond. Respectively, the construction of electrostatic potential and the derivation of the Schrodinger equation for the minimizer in these cases require an extra argument. The space-periodic ground states for 1D and 2D lattices give the model of the nanostructures similar to the carbon nanotubes and graphene, respectively. [ABSTRACT FROM AUTHOR]

We propose a new procedure for quantizing gauge fields that allows avoiding Gribov ambiguities and is therefore applicable outside the perturbation theory framework. We use this procedure to construct a gauge-invariant infrared regularization of the Yang-Mills theory. [ABSTRACT FROM AUTHOR]

We show that in the self-consistent equations for equal-time correlation functions of velocity fluctuations obtained in the model of developed turbulence based on the maximal randomness principle, infrared divergences are absent from all orders of the perturbation theory. We analyze the additional ultraviolet (UV) divergences that appear in the two-loop approximation of the self-consistent equations. We show that in the system with conserved parity, these divergences can be eliminated using the existing ambiguity in the solution. In the case of parity violation in the system, the UV divergences have a logarithmic form, which can indicate a deviation from the Kolmogorov scaling. [ABSTRACT FROM AUTHOR]

We construct a gauge-invariant infrared regularization of the Yang-Mills theory applicable beyond the perturbation theory. [ABSTRACT FROM AUTHOR]

The models of the $n\bar{n}$ transition in medium and nuclei based on the diagram technique for direct reactions, potential description of $\bar{n}$-medium interaction and field-theoretical approach are considered. It is shown that for the $n\bar{n}$ transition in medium field-theoretical approach should be used. The lower limit on the free-space $n\bar{n}$ oscillation time τ is in the range: 1016yr>τ>1.2⋅109s. [ABSTRACT FROM AUTHOR]

The model of $n\bar{n}$ transitions in the medium based on field-theoretical approach is considered. The time-dependence and corrections to the model are studied. The lower limit on the free-space $n\bar{n}$ oscillation time τ is in the range 1016yr>τ>1.2×109s. [ABSTRACT FROM AUTHOR]

The $n\bar{n}$ transitions for the neutrons in bound state are studied. The |in〉-state of nucleus is described by single-particle shell model. The dynamical process part is calculated by means of field-theoretical approach with finite time interval. The results are the same as for nuclear matter. [ABSTRACT FROM AUTHOR]

Abstract: Due to strong fluctuations, conventional approaches to handling repulsive spin-1/2 spin-waves in three dimensions do not work in low dimensions at temperature . We have constructed a renormalized theory for the two-dimensional spin-1/2 anisotropic quantum Heisenberg model by means of exact mappings between spin-1/2 systems and their corresponding hard-core Bose–Hubbard systems. With the t-matrix method, hard-core Bose–Hubbard systems can be effectively described by the corresponding soft-core Bose–Hubbard Hamiltonians at low energy. The method of running coupling constant in field theory is used to fix the infrared divergence due to long wavelength fluctuations in low dimensions at . Our results agree well with previous analytical and numerical works. The method dealing with infinities used by others in 3D is a special case of our renormalization scheme. Our approach works in both two and three dimensions at and . We think that our renormalization scheme is a more general and systematic approach in condensed matter physics. [Copyright &y& Elsevier]

Abstract: The Mumford process X is a stochastic distribution modulo constant and cannot be defined as a stochastic distribution invariant in law by dilations. We present two expansions of X—using wavelet bases—in which allow us to confine the divergence on the “small term” and which respect the invariance in law by dyadic dilations of the process. [Copyright &y& Elsevier]

Abstract: We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in dimensions can be removed at all orders of by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati–Testa model, resulting in a non-trivial conformal invariant field theory for all space–time dimensions . [Copyright &y& Elsevier]