Search

We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results are used to confirm the validity of a previously proposed analytical Ansatz for the initial state in the sinh-Gordon quench., 13 pages, 4 pdf figures

The generic feature of non-conformal fields in Poincare patch of de Sitter space is the presence of large IR loop corrections even for massive fields. Moreover, in global de Sitter there are loop IR divergences for the massive fields. Naive analytic continuation from de Sitter to Anti-de-Sitter might lead one to conclude that something similar should happen in the latter space as well. However, we show that there are no large IR effects in the one-loop two-point functions in the Poincare patch of Anti-de-Sitter space even for the zero mass minimally coupled scalar fields. As well there are neither large IR effects nor IR divergences in global Anti-de-Sitter space even for the zero mass., 12 pages. Minor changes, misprints are corrected

We study the light-front zero-mode contribution to the tensor form factors T i ( i = 1 , 2 , 3 ) for the exclusive rare P → V l + l − decays using a covariant fermion field theory model in ( 3 + 1 ) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ μ = γ μ − ( 2 k − P V ) μ / D , the three tensor form factors T i ( i = 1 , 2 , 3 ) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front energy or the longitudinal momentum fraction factor ( 1 / x ) n of the struck quark with the power n > 0 . Since the denominator D used in the light-front quark model (LFQM) has the power n = 1 / 2 , the three tensor form factors T i ( i = 1 , 2 , 3 ) can be computed in LFQM safely without involving any complicate zero-mode contribution. The lack of zero-mode contribution benefits the phenomenology with LFQM.

In this work, we discuss the cosmological evolutions in the nonrelativistic and possibly renormalizable gravitational theory, called the Hořava–Lifshitz (HL) theory. We consider the original HL model (type I), and the modified version obtained by an analytic continuation of parameters (type II). We classify the possible cosmological evolutions with arbitrary matter. We will find a variety of cosmology.

In this Letter, we calculate the next to the leading order Casimir energy for real massive and massless scalar fields within λ ϕ 4 theory, confined between two parallel plates with the Dirichlet boundary condition in two spatial dimensions. Our results are finite in both cases, in sharp contrast to the infinite result reported previously for the massless case. In this Letter we use a renormalization procedure introduced earlier, which naturally incorporates the boundary conditions. As a result our radiative correction term is different from the previously calculated value. We further use a regularization procedure which help us to obtain the finite results without resorting to any analytic continuation techniques.

We derive the two-loop QCD helicity amplitudes for the processes $l q \to l qg$ ($l \bar q \to l \bar q g$) and $l g \to l q\bar q$, which are the partonic reactions yielding $(2+1)$-jet final states in deep inelastic lepton nucleon scattering. The amplitudes are obtained by analytic continuation of the known helicity amplitudes for $e^+e^- \to q\bar q g$. We separate the infrared divergent and finite parts of the amplitudes using Catani's infrared factorization formula. The analytic results for the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms. To evaluate these functions numerically, we list in detail the non-trivial (and kinematic region dependent) variable transformations one needs to perform., Comment: 10 pages, LaTeX, typos corrected and references added, FORM and FORTRAN files with the helicity amplitudes are enclosed with the manuscript sources

The next to the leading order Casimir effect for a real scalar field, within ϕ 4 theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Green's function with the Dirichlet boundary condition on both walls. In this Letter we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms, in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. We obtain finite results for the massive and massless cases, in sharp contrast to some of the other reported results. Secondly, and probably less importantly, we use a supplementary renormalization procedure in addition to the usual regularization and renormalization programs, which makes the usage of any analytic continuation techniques unnecessary.

The Hawking emissivities for the scalar-, vector-, and tensor-mode bulk gravitons are computed in the full range of the graviton's energy by adopting the analytic continuation numerically when the spacetime background is $(4+n)$-dimensional non-rotating black hole. The total emissivity for the gravitons is only 5.16% of that for the spin-0 field when there is no extra dimension. However, this ratio factor increases rapidly when the extra dimensions exist. For example, this factor becomes 147.7%, 595.2% and 3496% when the number of extra dimensions is 1, 2 and 6, respectively. This fact indicates that the Hawking radiation for the graviton modes becomes more and more significant and dominant with increasing the number of extra dimensions., Comment: 14 pages, 5 eps figures, V2: the incorrect multiplicities are corrected. PLB version

We derive semi--analytic expressions for the analytic continuation of the Mellin transforms of the heavy flavor QCD coefficient functions for neutral current deep inelastic scattering in leading and next-to-leading order to complex values of the Mellin variable $N$. These representations are used in Mellin--space QCD evolution programs to provide fast evaluations of the heavy flavor contributions to the structure functions $F_2(x,Q^2), F_L(x,Q^2)$ and $g_1(x,Q^2)$., 13 pages Letex, 1 style file, 10 eps figures

We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The power of the method is illustrated by calculating the imaginary parts of the partition function of the anharmonic oscillator in zero spacetime dimensions and of the ground state energy of the anharmonic oscillator for all negative values of the coupling constant g and show that they are in excellent agreement with the exactly known values. As a highlight of the theory we recover from the divergent perturbation expansion of the tunnelling amplitude the action of the instanton and the effects of higher loop fluctuations around it.

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part., Comment: 8 pages, latex

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $\Phi_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models., Comment: 13pgs, harvmac, 2 figs

Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known results of the interplay of them are reproduced naturally. The prescription for separating the non-perturbative contribution from the perturbative is given in terms of the analytic continuation of the valley parameter. Our method is illustrated on a new series of examples with the asymmetric double-well potential. We obtain the non-perturbative part explicitly, which leads to the prediction of the large order behavior of the perturbative series. We calculate the first 200 perturbative coefficients for a wide range of parameters and confirm the agreement with the prediction of the valley method., 13 pages, 4 eps figures, LaTeX, gzipped tar file

The analytic continuation by duality (ACD) technique has been used to estimate the electroweak S parameter in technicolor models. In this letter, we investigate the reliability of this method by applying it to some toy models with known spectra. We find that in most instances the technique cannot be trusted to give a reliable result., Comment: 15 pages, LaTeX, 2 postscript figures. Uses seceqn.sty and epsfig.sty

We comment on the structure of intersecting black p-brane solutions in string theory explaining how known solutions can be obtained from Schwarzschild solution simply by sequences of boosts and dualities. This implies, in particular, that dimensional reduction in all internal world-volume directions including time leads to a metric (related by analytic continuation to a cosmological metric) which does not depend on p-brane charges, i.e. is the same as the metric following by reduction from a higher-dimensional `neutral' Schwarzschild black hole., Comment: 6 pages, harvmac. Misprints corrected, version to appear in Physics Letters

Unsubtracted dispersion relations are used to link new data obtained in the time-like region with the electromagnetic structure of the nucleons as measured in the space-like region. Simple analytic representations of the magnetic form factor of the proton GpM(Q2) and the electric form factor of the neutron GnE(Q2) are derived which have the following properties built-in: the correct normalization and slope at Q2 = 0 and correct asymptotic behavior at |Q2| → ∞. The pred of perturbative QCD at asymptotic Q2 and meson physics at low Q2 are combined to fit the existing data in the entire range of the four-momentum transfer squared. This leads to the following observations: (i) Measurements of cross sections for the reaction p p → e + e − taken at the Fermilab E-760 match measurements made at the SLAC-136 experiment only if the logarithmic falloff of Q4GpM(Q2), expected from leading twist predictions of perturbative quantum chromodynamics, is included. (ii) Analytic continuation of the neutron time-like form factor into the space-like interval 0.1 GeV2 ≤ Q2 ≤ 1 GeV2 using the limited FENICE data gives a factor of ∼ 2 inconsistency in GnE(Q2) with the recent Saclay and Mainz measurements.

We investigate the Ward identities of the $W_{\infty}$ symmetry in the Liouville theory coupled to the $(p,q)$ conformal matter. The correlation functions are defined by applying the analytic continuation procedure for the matter sector as well as the Liouville one. We then find that the Ward identities are equivalent to the $W_q$ algebra constraints deduced from the matrix model.

We introduce a modified form of dimensional regularization which manifestly preserves gauge invariance, unitarity, and global supersymmetry. The prescription is that the action which results from analytic continuation to lower dimensions is that found by dimensional reduction. We also consider its application to supergravity.

Analytic continuation in the bare Pomeron intercept is discussed in the context of a representation of the Pomeron propagator derived by the renormalization-group approach. When the bare intercept is above the critical value, the leading singularity turns out to be a branch point fixed at J = 1. The resulting cross section grows like (ln s ) r . where r is a ratio of critical exponents. In the one- and two-loop approximations, r ≈ 1.

It is shown that the principle of analytic continuation is well suited for regulating the spurious singularity peculiar to Feynman integrals in the axial gauges. This new, analytic regularization is much more powerful than the standard regularization based on the principal-value prescription, at the same time yielding identical results compared to the latter. An analytic representation based on a Meijer G-function is derived for the class of massless, two-point integrals ∫d2ωq[(p − q)2] κ × (q2)μ(q · n)v, where n is the vector defining the axial guage and ω, κ, μ and v are continuous variables. Several important aspects of the representation are discussed and examples of its application are given.

Complex probabilities arise in quantum systems where the euclidean action is complex, either because the couplings, or the field variables, are complex. Stochastic quantization using the Langevin equation allows one to study such systems, even though the probabilistic interpretation of the euclidean functional integral measure breaks down. The convegence of long time averages computed with the Langevin equation to the analytic continuation of the functional integral averages is investigated for some simple models. The proposed methods have a variety of applications, including nonperturbative studies of chiral gauge theories on the lattice.

The method of approximate analytic continuation by duality (ACD), which permits to extrapolate a two-point function from its asymptotic QCD form down to Q2 = 0, is used to determine the value of the light quark masses in QCD. For the value of the four-quark condensate advocated by Shifman, Vainshtein and Zakharov we obtain (mu + md) = (21 ± 2) MeV at Q2 = 1 GeV2.

We perform the analytic continuation, from the scattering ( t t > 0) region, of the non-planar diagrams (having torus topology) which generate a splitting between planar trajectories with non-zero iso-spin. Using heavily our previous work on the planar and cylinder amplitudes, we derive “asymptotic planarity” and estimate the rate of approach to it, also for the torus under rather general assumption on the Reggeon-Reggeon amplitude fixed pole residue.

The path integral for the gravity sector of supergravity, i.e., after integration over the spin- 3 2 field, is formally shown to be governed by the linearized Einstein action in terms of redefined field variables. The exponential of the action now being a product of gaussians, positivity of the action in euclidean signature is simply achieved by analytic continuation in those field components whose squares initially appear with the wrong sign.

In the framework of the cut vertex formalism we present the results of calculations of the quantities needed for a next to leading logarithmic analysis of scaling violations for structure and fragmentation functions in Quantum Chromodynamics. We find that an analytic continuation relation holds, between the time and space like regions, while the Gribov-Lipatov reciprocity relation is violated.

We announce the solution of the old problem of relativistic quantum field theory, namely the (nonperturbative) construction of interacting local relativistic quantum fields over four-dimensional spacetime satisfying all axioms. The fields are obtained starting from euclidean random fields satisfying systems of coupled stochastic partial differential equations. Using their Markov property with respect to three-dimensional hyperplanes and gauge invariance, we construct from these fields new euclidean random fields which are Osterwalder-Schrader reflection positive, yielding a symmetric contraction semigroup generated by a positive hamiltonian on a L 2 -space of gauge invariant functions. The relativistic fields are then obtained by analytic continuation. The constructed fields are interacting, asymptotically free and are the continuum limits of lattice fields. An expression for their hamiltonian is provided.

The conformal field theory of analytic differentials on a general Riemann surface is formulated. All the determinants and correlation functions are expressed in terms of theta-functions.

A report is made on a new attempt to determine analytic continuation of scattering amplitudes, which consists of evaluating iteratively on a computer the usual dispersion relation and its inverted one. Its application to the pp forward amplitude shows that this method is practical and powerful. Its imaginary part is shown to have a large dip just above the p p threshold, which makes its high-energy real part nearly twice that determined experimentally ignoring spin-flip.

We prove that the energy levels of an arbitrary anharmonic oscillator ( x 2 m and in any finite number of dimensions) are determined uniquely by their Rayleigh-Schrodinger series via a (generalized) Borel summability method. To use this method for computations, one must make an analytic continuation which we accomplish by (a rigorously unjustified) use of Pade approximants in the case of p 2 + x 2 + β x 4 . The numerical results appear to be better than with the direct use of Pade approximants.

Proceeding from the analytic continuation of the Lippmann-Schwinger integral equation onto the unphysical energy sheet, a new simple formula for the residue of the t -matrix in the pole on the unphysical sheet is derived. The formula expresses the residue in terms of the partial scattering amplitude at the corresponding energy point on the physical sheet. For the Yukawa type potential a new symmetry theorem for bound and virtual levels is proved. The theorem makes it possible to indicate the points on level trajectories which are mirror-symmetrical with respect to zero momentum.

An analytic continuation procedure is proposed for cross-sections and density matrix elements to discuss their possible kinematical singularities. As expected, the s channel cross-section even when expressed in terms of the t channel amplitudes is free from kinematical singularities in the t variable whereas the density matrix elements in the Jackson frame can be singular at the t channel thresholds and pseudothresholds.