Temporal correlator in YM32 and reflection-positivity violation

We consider numerical data for the lattice Landau gluon propagator obtained at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge theory (YM32). We find that the temporal correlator C(t) shows an oscillatory pattern and is negative for several values of t. This is an explicit violation of reflection positivity and can be related to gluon confinement. We also obtain a good fit for this quantity in the whole time interval using a sum of Stingl-like propagators.

Scalar field theory at finite temperature in D=2+1

We discuss the phi(6) theory defined in D = 2 + 1-dimensional space-time and assume that the system is in equilibrium with a thermal bath at temperature beta(-1). We use the 1/N expansion and the method of composite operator (CJT) for summing a large set of Feynman graphs. We demonstrate explicitly the Coleman-Mermin-Wagner theorem at finite temperature.

Light Front Boson Model Propagation

The scope and aim of this work is to describe the two-body interaction mediated by a particle (either the scalar or the gauge boson) within the light-front formulation. To do this, first of all we point out the importance of propagators and Green functions in Quantum Mechanics. Then we project the covariant quantum propagator onto the light front time to get the propagator for scalar particles in these coordinates. This operator propagates the wave function from x(+) = 0 to x(+) > 0. It corresponds to the definition of the time ordering operation in the light front time x(+). We calculate the light-front Green's function for 2 interacting bosons propagating forward in x(+). We also show how to write down the light front Green's function from the Feynman propagator and finally make a generalization to N bosons.

Do tadpoles vanish in the light-front?

In covariant gauges (CG) regularized with dimensional regularization (DR) it is a standard procedure to set all tadpole Feynman integrals to zero, though; explicitly, they diverge quadratically as the space-time volume. on the other hand, in the notoriously subtle light-front gauge (LTG) some divergent tadpole integrals are said to be nonvanishing, i.e., cannot be set to zero as in the CC case. In this article we analyse the reasons behind this seemingly ambiguous results.

Why Pair Production Cures Covariance in the Light-Front?

We show that the light-front vacuum is not trivial, and the Fock space for positive energy quanta solutions is not complete. As an example of this non triviality we have calculated the electromagnetic current for scalar bosons in the background field method were the covariance is restored through considering the complete Fock space of solutions.In this work we construct the electromagnetic current operator for a system composed of two free bosons. The technique employed to deduce these operators is through the definition of global propagators in the light front when a background electromagnetic field acts on one of the particles.

LOW-ENERGY BEHAVIOR OF FEW-PARTICLE SCATTERING-AMPLITUDES IN 2 DIMENSIONS

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of ph cal interest.

Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

Analytic properties of thermal corrected boson propagators

We investigate the analytic properties of finite-temperature self-energies of bosons interacting with fermions at one-loop order. A simple boson-fermion model was chosen due to its interesting features of having two distinct couplings of bosons with fermions. This leads to a quite different analytic behavior of the bosons self-energies as the external momentum K-mu=(k(0),k) approaches zero in the two possible limits. It is shown that the plasmon and Debye masses are consistently obtained at the pole of the corrected propagator even when the self-energy is analytic at the origin in the frequency-momentum space.

On the quantum Hamilton-Jacobi formalism

Some postulates are introduced to go from the classical Hamilton-Jacobi theory to the quantum one. We develop two approaches in order to calculate propagators, establishing the connection between them and showing the equivalence of this picture with more known ones such as the Schrödinger's and the Feynman's formalisms. Applications of the above-mentioned approaches to both the standard case of the harmonic oscillator and to the harmonic oscillator with time-dependent parameters are made. © 1991 Plenum Publishing Corporation.

The propagator for a charged oscillator with a time-dependent mass in a time-varying electromagnetic field

We make a change of variables and a time reparametrization in the Schrödinger equation in order to obtain the propagator of a charged oscillator with a time-dependent mass and frequency under the influence of time-varying electric and magnetic fields, in terms of the simple propagators of harmonic oscillators with constant frequencies and masses. We also discuss the Jackiw transformation and others as a particular case of ours. © 1991.

Two-loop self-energy diagrams worked out with NDIM

In this work we calculate two two-loop massless Feynman integrals pertaining to self-energy diagrams using NDIM (Negative Dimensional Integration Method). We show that the answer we get is 36-fold degenerate. We then consider special cases of exponents for propagators and the outcoming results compared with known ones obtained via traditional methods.

Leading particle effect, inelasticity, and the connection between average multiplicities in e+e- and pp processes

The Regge-Mueller formalism is used to describe the inclusive spectrum of the proton in pp collisions. From such a description the energy dependences of both average inelasticity and leading proton multiplicity are calculated. These quantities are then used to establish the connection between the average charged particle multiplicities measured in e+e- and pp/p̄p processes. The description obtained for the leading proton cross section implies that Feynman scaling is strongly violated only at the extreme values of xF, that is at the central region (xF≈0) and at the diffraction region (XF≈1), while it is approximately observed in the intermediate region of the spectrum. ©1999 The American Physical Society.

Relativistic quark spin coupling effects in the nucleon electromagnetic form factors

We investigate the effect of different forms of relativistic spin coupling of constituent quarks in the nucleon electromagnetic form factors. The four-dimensional integrations in the two-loop Feynman diagram are reduced to the null-plane, such that the light-front wave function is introduced in the computation of the form factors. The neutron charge form factor is very sensitive to different choices of spin coupling schemes, once its magnetic moment is fitted to the experimental value. The scalar coupling between two quarks is preferred by the neutron data, when a reasonable fit of the proton magnetic momentum is found. (C) 2000 Elsevier Science B.V.

Quadratic effective action for QED in D=2,3 dimensions

We calculate the effective action for quantum electrodynamics (QED) in D=2,3 dimensions at the quadratic approximation in the gauge fields. We analyze the analytic structure of the corresponding nonlocal boson propagators nonperturbatively in k/m. In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson. We also calculate in D=2 the effective potential between two static charges separated by a distance L and find it to be a linearly increasing function of L in agreement with the bosonized theory (massive sine-Gordon model). In three dimensions we find nonperturbatively in k/m one massive pole in the effective bosonic action leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimensionless parameter e2/m. ©2000 The American Physical Society.

First results for the Coulomb gauge integrals using NDIM

The Coulomb gauge has at least two advantages over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations, are not well defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into D = ω + ρ, i.e., introducing a specific parameter ρ to regulate the energy integrals. The aim of our work is to apply the negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results - finite and divergent parts - to the one- and two-loop level for arbitrary exponents of the propagators and dimension.