Martin Schaden

Landau gauge within the Gribov horizon.

We consider a model which effectively restricts the functional integral of Yang-Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as the ordinary Yang-Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the BRS symmetry.

Equivariant gauge fixing of SU(2) lattice gauge theory

I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group and an equivariant BRST symmetry that is physically equivalent to the standard SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete symmetries of the lattice and its partition function does not vanish. The Topological Lattice Theories (TLT) that localize on the moduli spaces are explicitly constructed and their BRST symmetry is exhibited. The ghosts of the Z_2-invariant local LGT are integrated in favor of a nonlocal bosonic measure. In addition to the SU(2) link variables and the coupling g^2, this effective bosonic measure also depends on an auxiliary gauge invariant site variable of canonical dimension two and on a gauge parameter \alpha. The relation between the expectation value of the auxiliary field, the gauge parameter \alpha and the lattice spacing

Living with spontaneously broken BRST symmetry. I. Physical states and cohomology

a

Infrared saturation and phases of gauge theories with BRST symmetry.

is obtained to lowest order in the loop expansion. In four dimensions and the critical limit this expectation value is a physical scale proportional to \Lambda_L in the gauge \alpha=g^2 (11-n_f)/24+ O(g^4). Implications for the loop expansion of observables in such a critical gauge are discussed.

GAUGE GROUP TQFT AND IMPROVED PERTURBATIVE YANG–MILLS THEORY

We address the issue of BRST symmetry breaking in the GZ model, a local, renormalizable, non-perturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRST-exact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model, and obtain a useful sufficient condition that determines which operators preserve BRST. Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened, and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory. PACS numbers: 11.15.-q,11.15.Tk ∗ mschaden@rutgers.edu † dz2@nyu.edu

Topological aspects of gauge-fixing Yang-Mills theory on {ital S}{sub 4}

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo–Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov–Zwanziger theory.

Semiclassical estimates of electromagnetic Casimir self-energies of spherical and cylindrical metallic shells

We reinterpret the Faddeev–Popov gauge-fixing procedure of Yang–Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating topological gauge-fixing ambiguities to the global breaking of a supersymmetry. The global zero modes of the Faddeev–Popov ghosts are handled in the context of an equivariant cohomology without breaking translational invariance. The gauge-fixing involves constant fields which play the role of moduli and modify the behavior of Green functions at subasymptotic scales. At the one loop level physical implications from these power corrections are gauge invariant.

Heavy quark decomposition of the S matrix and its relation to the pinch technique.

For an {ital S}{sub 4} space-time manifold global aspects of gauge fixing are investigated using the relation to topological quantum field theory (TQFT) on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solutions to a covariant gauge conditon on the orbit of a particular instanton are found using the SO(5) isometry group of the {ital S}{sub 4} base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that an orbit with a Pontryagin number {kappa}={plus_minus}1 in covariant gauges on {ital S}{sub 4} contributes to physical correlation functions with a different multiplicity factor due to the Gribov copies than an orbit in the trivial {kappa}=0 sector. Similar topological arguments show that there is no contribution from the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discuss the possible physical implications of the global gauge dependence of Yang-Mills theory. {copyright} {ital 1996 The American Physical Society.}

Living with spontaneously broken BRST symmetry. II. Poincaré invariance

The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries, and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically, the nonvanishing Casimir energy of a metallic cylindrical shell is almost entirely due to Fresnel diffraction.

Diffraction in the semiclassical approximation to Feynman's path integral representation of the Green function

We propose a decomposition of the {ital S} matrix into individually gauge invariant subamplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompoosition is obtained by considering limits of the {ital S} matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge-independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic {ital n}-point functions is briefly discussed.