22 research outputs found
The pseudoparticle approach for solving path integrals in gauge theories
We present a numerical technique for calculating path integrals in
non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by
a superposition of pseudoparticles of various types with their amplitudes and
color orientations as degrees of freedom. Applied to Maxwell theory this
technique results in a potential which is in excellent agreement with the
Coulomb potential. For SU(2) Yang-Mills theory the same technique yields clear
evidence of confinement. Varying the coupling constant exhibits the same
scaling behavior for the string tension, the topological susceptibility and the
critical temperature while their dimensionless ratios are similar to those
obtained in lattice calculations.Comment: Talk presented at Lattice 2005 (Topology and Confinement), 6 pages, 4
figure
Topological Concepts in Gauge Theories
In these lecture notes, an introduction to topological concepts and methods
in studies of gauge field theories is presented. The three paradigms of
topological objects, the Nielsen-Olesen vortex of the abelian Higgs model, the
't Hooft-Polyakov monopole of the non-abelian Higgs model and the instanton of
Yang-Mills theory, are discussed. The common formal elements in their
construction are emphasized and their different dynamical roles are exposed.
The discussion of applications of topological methods to Quantum Chromodynamics
focuses on confinement. An account is given of various attempts to relate this
phenomenon to topological properties of Yang-Mills theory. The lecture notes
also include an introduction to the underlying concept of homotopy with
applications from various areas of physics.Comment: Lecture note
Chiral Condensate and Short-Time Evolution of QCD(1+1) on the Light-Cone
Chiral condensates in the trivial light-cone vacuum emerge if defined as
short-time limits of fermion propagators. In gauge theories, the necessary
inclusion of a gauge string in combination with the characteristic light-cone
infrared singularities contain the relevant non-perturbative ingredients
responsible for formation of the condensate, as demonstrated for the 't Hooft
model.Comment: 4 pages, Revtex
Phases and Residual Gauge Symmetries of Higgs Models
After elimination of the redundant variables, gauge theories may still
exhibit symmetries associated with the gauge fields. The role of these residual
gauge symmetries is discussed within the Abelian Higgs model and the
Georgi-Glashow model. In the different phases of these models, these symmetries
are realized differently. The characteristics of emergence and disappearance of
the symmetries are studied in detail and the implications for the dynamics in
Coulomb, Higgs, and confining phases are discussed.Comment: 30 pages, LaTeX with amsmath macros; updated to include minor
corrections in proof; email correspondence to J.W. Negele,
[email protected]
The Casimir Effect on the Light-Cone
The Casimir effect is investigated in light-cone quantization. It is shown
that for spacelike separation of the walls enclosing the system the standard
result for the pressure exerted on the walls is obtained. For walls separated
in light-cone space direction no regularization of the quantum fluctuations
exists which would yield a finite pressure. The origin of this failure and its
implications for other vacuum properties are discussed by analyzing the Casimir
effect as seen from a moving observer approaching the speed of light. The
possibility for calculation of thermodynamic quantities in light-cone
quantization via the Casimir effect is pointed out
Magnetic and Thermodynamic Stability of SU(2) Yang-Mills Theory
SU(2) Yang-Mills theory at finite extension or, equivalently, at finite
temperature is probed by a homogeneous chromomagnetic field. We use a recent
modified axial gauge formulation which has the novel feature of respecting the
center symmetry in perturbation theory. The characteristic properties of the
Z_2-symmetric phase, an extension-dependent mass term and antiperiodic boundary
conditions, provide stabilization against magnetic field formation for
sufficiently small extension or high temperature. In an extension of this
investigation to the deconfined phase with broken center symmetry, the combined
constraints of thermodynamic and magnetic stability are shown to yield many of
the high temperature properties of lattice SU(2) gauge theory.Comment: 27 pages, LATEX, 7 postscript figures, corrected typo
Chiral Condensates in the Light-Cone Vacuum
In light-cone quantization, the standard procedure to characterize the phases
of a system by appropriate ground state expectation values fails. The
light-cone vacuum is determined kinematically. We show that meaningful
quantities which can serve as order parameters are obtained as expectation
values of Heisenberg operators in the equal (light-cone) time limit. These
quantities differ from the purely kinematical expectation values of the
corresponding Schroedinger operators. For the Nambu--Jona-Lasinio and the
Gross-Neveu model, we describe the spontaneous breakdown of chiral symmetry; we
derive within light-cone quantization the corresponding gap equations and the
values of the chiral condensate.Comment: Latex, 9 pages, no figur