Search

Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an SU(3) gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios., Comment: 22 pages, 9 figures

Within the refined Gribov-Zwanziger scenario for four-dimensional Yang-Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that simply adding a gluon mass term to the usual Faddeev-Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in good agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators., Comment: 81 pages, 30 figures

In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of the numerical approximation of the non-relativistic path integral, resulting in a formalism whose characteristic feature is the fast, non-recursive generation of an ensemble of trajectories that is independent of the potential, and thus universally applicable. The numerical implementation discretises the trajectories with respect to their time parametrisation but maintains a continuous spatial domain. In the case of singular potentials, the discretised action gets adapted to the singularity through a "smoothing" procedure. We show for a variety of examples (the harmonic oscillator in various dimensions, the modified P\"oschl-Teller potential, delta-function potentials, the Coulomb and Yukawa potentials) that the method allows one to obtain fast and reliable estimates for the Euclidean propagator and use them in a certain time window suitable for extracting the ground state energy. As an aside, we apply it for studying the classical limit where nearly classical trajectories are expected to dominate in the path integral. We expect the advances made here to be useful also in the relativistic case., Comment: 51 + 13 pages. Many figures

We introduce two new integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path averaged potential)., Comment: 8 pages, 4 figures, 2 appendices. Updated to published version

We study the ground state energy and the critical screening parameter of the Yukawa potential in non-relativistic quantum mechanics. After a short review of the existing literature on these quantities, we apply fifth-order perturbation theory to the calculation of the ground state energy, using the exact solutions of the Coulomb potential together with a cutoff on the principal number summations. We also perform a variational calculation of the ground state energy using a Coulomb-like radial wave function and the exact solution of the corresponding minimization condition. For not too large values of the screening parameter, close agreement is found between the perturbative and variational results. For the critical screening parameter, we devise a novel method that permits us to determine it to ten digits. This is the most precise calculation of this quantity to date, and allows us to resolve some discrepancies between previous results., Comment: 16 pages, 7 figures

Over the last decade, the infrared behavior of Yang-Mills theory in the Landau gauge has been scrutinized with the help of Dyson-Schwinger equations and lattice calculations. In this contribution, we describe a technically simple approach to the deep infrared regime via Callan-Symanzik renormalization group equations in an epsilon expansion. This approach recovers, in an analytical and systematically improvable way, all the solutions previously found as solutions of the Dyson-Schwinger equations and singles out the solution favored by lattice calculations as the infrared-stable fixed point (for space-time dimensions above two)., Comment: 6 pages, talk delivered at the conference Light Cone 2012 in Cracow, Poland

The infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory has been at the center of an intense debate over the last decade. Different solutions of the Dyson-Schwinger equations show a different behavior of the propagators in the infrared: in the so-called scaling solutions both propagators follow a power law, while in the decoupling solutions the gluon propagator shows a massive behavior. The latest lattice results favor the decoupling solutions. In this contribution, after giving a brief overview of the present status of analytical and semi-analytical approaches to the infrared regime of Landau gauge Yang-Mills theory, we will show how Callan-Symanzik renormalization group equations in an epsilon expansion reproduce both types of solutions and single out the decoupling solutions as the infrared-stable ones for space-time dimensions greater than two, in agreement with the lattice calculations., Comment: 17 pages. Talk delivered at the XIII Mexican Workshop on Particles and Fields in Leon, Guanajuato, Mexico, October 2011. Slightly extended version of the contribution to the conference proceedings

The study of the Dyson-Schwinger equations of Landau gauge Yang-Mills theory has revealed two types of solutions for the gluon and ghost propagators, with a scaling and a massive (decoupling) behavior in the extreme infrared, respectively. We show that both types of solutions are quantitatively reproduced by applying renormalization group equations of Callan-Symanzik type in an epsilon expansion to the infrared limit of Landau gauge Yang-Mills theory when a mass term for the gluons is added to the action. Only the decoupling solution corresponds to an infrared-stable fixed point in three and four space-time dimensions and is hence expected to be physically realized, in agreement with the results of recent lattice calculations., Comment: 12 pages, LaTeX; several short comments and references added; to be published in Phys. Rev. D

We consider the Hamiltonian formulation of Yang-Mills theory in the Coulomb gauge and apply the recently developed technique of Hamiltonian flows. We formulate a flow equation for the color Coulomb potential which allows for a scaling solution that results in an almost linearly rising confining potential., Comment: 6 pages, 4 figures

A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach., Comment: 3 pages, talk presented at the conference "Quark Confinement and the Hadron Spectrum IX", August 30 - September 3, 2010, Madrid, to appear in the AIP proceedings

A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach., Comment: 7 pages, 7 figures. Talk presented by H. Reinhardt at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 2010

We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed., Comment: 17 pages, 10 figures

We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static colour sources are calculated to one-loop order. Furthermore, the one-loop $\beta$-function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory., Comment: 15 pages, 3 figures

A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary masses). We compare the spectrum for the relativistic value alpha = 0.3 with corresponding calculations in light-front quantization., Comment: 6 pages, LaTeX, 2 figures, uses aipxfm.sty. Talk delivered at the XI Mexican Workshop on Particles and Fields, Tuxtla Gutierrez, Mexico, November 7-12, 2007; to be published in the proceedings

We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop quantized theories is constructed as a continuum limit of dynamics of effective theories. After presenting the general formalism we show as first explicit example the 2d Ising field theory. It is an interacting relativistic quantum field theory with local degrees of freedom quantized by loop quantization techniques., Comment: 14 pages, no figures

A generalization of the Gell-Mann-Low Theorem is applied to bound state calculations in Yukawa theory. The resulting effective Schroedinger equation is solved numerically for two-fermion bound states with the exchange of a massless boson. The complete low-lying bound state spectrum is obtained for different ratios of the constituent masses. No abnormal solutions are found. We show the consistency of the non-relativistic and one-body limits and discuss the special cases of identical fermions and fermion-antifermion states. To our knowledge, this is the first consistent calculation of bound states in pure Yukawa theory (without UV cutoff)., Comment: 62 pages, 6 eps figures

We study the realization of dimensional reduction and the validity of the hard thermal loop expansion for lambda phi^4 theory at finite temperature, using an environmentally friendly finite-temperature renormalization group with a fiducial temperature as flow parameter. The one-loop renormalization group allows for a consistent description of the system at low and high temperatures, and in particular of the phase transition. The main results are that dimensional reduction applies, apart from a range of temperatures around the phase transition, at high temperatures (compared to the zero temperature mass) only for sufficiently small coupling constants, while the HTL expansion is valid below (and rather far from) the phase transition, and, again, at high temperatures only in the case of sufficiently small coupling constants. We emphasize that close to the critical temperature, physics is completely dominated by thermal fluctuations that are not resummed in the hard thermal loop approach and where universal quantities are independent of the parameters of the fundamental four-dimensional theory., Comment: 20 pages, 13 eps figures, uses epsfig and pstricks

In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger representation, and similarity transformation methods for Hamiltonian approaches in light-front quantization. Finally, I will comment on a related similarity transformation in the usual equal-time quantized theory., Comment: 9 pages, LaTeX, 3 pspicture diagrams, 3 postscript figures, uses aipxfm.sty. Talk delivered at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 2002

The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem retains, while being fully relativistic, many of the desirable features of the quantum mechanical approaches to bound states. In particular, no abnormal or unphysical solutions are found in the model under consideration. Both the non-relativistic and one-body limits are straightforward and consistent. The results for the spectrum are compared to those of the Bethe-Salpeter equation (in the ladder approximation) and related equations., Comment: 24 pages, 6 pspicture diagrams, 4 postscript figures

The effective Hamiltonian introduced many years ago by Bloch and generalized later by Wilson, appears to be the ideal starting point for Hamiltonian perturbation theory in quantum field theory. The present contribution derives the Bloch-Wilson Hamiltonian from a generalization of the Gell-Mann-Low theorem, thereby enabling a diagrammatic analysis of Hamiltonian perturbation theory in this approach., Comment: 5 pages, LaTeX, uses aipproc.sty. Talk delivered at the VII Mexican Workshop on Particles and Fields, Merida, Yucatan, November 10-17, 1999; to be published in the proceedings

We examine the relation between the damping rate of a chiral fermion mode propagating in a hot plasma and the rate at which the mode approaches equilibrium. We show how these two quantities, obtained from the imaginary part of the fermion self-energy, are equal when the reaction rate is defined using the appropriate wave function of the mode in the medium. As an application, we compute the production rate of hard axions by Compton-like scattering processes in a hot QED plasma starting from both, the axion self-energy and the electron self-energy. We show that the latter rate coincides with the former only when this is computed using the corresponding medium spinor modes., Comment: Modified version, includes new section on the hard axion photoproduction rate in a hot QED plasma. Version to appear in Int. Jour. Mod. Phys. A

We perform a calculation of the full momentum dependence of the gluon and ghost propagators in pure SU(3) Yang-Mills theory by integrating Wilson's exact renormalization group equations with respect to an infrared cutoff k. The heavy quark potential in the quenched approximation can be expressed in terms of these propagators. Our results strongly indicate a 1/p^4 behaviour of the heavy quark potential for $p^2 \to 0$. We show in general, that effective actions which satisfy Schwinger-Dyson equations, correspond to (quasi-) fixed points of Wilson's exact renormalization group equations., Comment: 33 pages, 9 figs, (Comments on the compatibility of the approximations with BRST invariance have been added)