24 research outputs found
On the Geometrical Structure of Covariant Anomalies in Yang-Mills Theory
Covariant anomalies are studied in terms of the theory of secondary
characteristic classes of the universal bundle of Yang-Mills theory. A new set
of descent equations is derived which contains the covariant current anomaly
and the covariant Schwinger term. The counterterms relating consistent and
covariant anomalies are determined. A geometrical realization of the
BRS/anti-BRS algebra is presented which is used to understand the relationship
between covariant anomalies in different approaches.Comment: 19 pages, LMU-TPW 92-31 (January 93
Field Space Entanglement Entropy, Zero Modes and Lifshitz Models
The field space entanglement entropy of a quantum field theory is obtained by
integrating out a subset of its fields. We study an interacting quantum field
theory consisting of massless scalar fields on a closed compact manifold M. To
this model we associate its Lifshitz dual model. The ground states of both
models are invariant under constant shifts. We interpret this invariance as
gauge symmetry and subject the models to proper gauge fixing. By applying the
heat kernel regularization one can show that the field space entanglement
entropies of the massless scalar field model and of its Lifshitz dual are
agreeing.Comment: 13 pages, revised and extended version, accepted for publication in
Physics Letters
Aspects of Higher-Abelian Gauge Theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops
Higher-abelian gauge theories associated with Cheeger-Simons differential
characters are studied on compact manifolds without boundary. The paper
consists of two parts: First the functional integral formulation based on zeta
function regularization is revisited and extended in order to provide a general
framework for further applications. A field theoretical model - called extended
higher-abelian Maxwell theory - is introduced, which is a higher-abelian
version of Maxwell theory of electromagnetism extended by a particular
topological action. This action is parametrized by two non-dynamical harmonic
forms and generalizes the -term in usual gauge theories. In the second
part the general framework is applied to study the topological Casimir effect
in higher-abelian gauge theories at finite temperature at equilibrium. The
extended higher-abelian Maxwell theory is discussed in detail and an exact
expression for the free energy is derived. A non-trivial topology of the
background space-time modifies the spectrum of both the zero-point fluctuations
and the occupied states forming the thermal ensemble. The vacuum (Casimir)
energy has two contributions: one related to the propagating modes and the
second one related to the topologically inequivalent configurations of
higher-abelian gauge fields. In the high temperature limit the leading term is
of Stefan-Boltzmann type and the topological contributions are suppressed. With
a particular choice of parameters extended higher-abelian Maxwell theories of
different degrees are shown to be dual. On the -dimensional torus we provide
explicit expressions for the thermodynamic functions in the low- and high
temperature regimes, respectively. Finally, the impact of the background
topology on the two-point correlation function of a higher-abelian variant of
the Polyakov loop operator is analyzed.Comment: v2: typos corrected; Version accepted for publication in Nucl. Phys.
B; 56 page
Global Path Integral Quantization of Yang-Mills Theory
Based on a generalization of the stochastic quantization scheme recently a
modified Faddeev-Popov path integral density for the quantization of Yang-Mills
theory was derived, the modification consisting in the presence of specific
finite contributions of the pure gauge degrees of freedom. Due to the Gribov
problem the gauge fixing can be defined only locally and the whole space of
gauge potentials has to be partitioned into patches. We propose a global path
integral density for the Yang-Mills theory by summing over all patches, which
can be proven to be manifestly independent of the specific local choices of
patches and gauge fixing conditions, respectively. In addition to the
formulation on the whole space of gauge potentials we discuss the corresponding
global path integral on the gauge orbit space relating it to the original
Parisi-Wu stochastic quantization scheme and to a proposal of Stora,
respectively.Comment: 8 pages, Latex, extended versio
QED Revisited: Proving Equivalence Between Path Integral and Stochastic Quantization
We perform the stochastic quantization of scalar QED based on a
generalization of the stochastic gauge fixing scheme and its geometric
interpretation. It is shown that the stochastic quantization scheme exactly
agrees with the usual path integral formulation.Comment: 11 page