27 research outputs found
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
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
Quantizing Yang-Mills Theory: From Parisi-Wu Stochastic Quantization to a Global Path Integral
Based on a generalization of the stochastic quantization scheme we recently
proposed a generalized, globally defined Faddeev-Popov path integral density
for the quantization of Yang-Mills theory. In this talk first our approach on
the whole space of gauge potentials is shortly reviewed; in the following we
discuss the corresponding global path integral on the gauge orbit space
relating it to the original Parisi-Wu stochastic quantization scheme.Comment: 4 pages, Latex, uses espcrc2.sty; talk by Helmuth Huffel at the Third
Meeting on Constrained Dynamics and Quantum Gravity, Villasimius, Sardinia,
Italy, Sept. 13-17, 199
Generalized Stochastic Quantization of Yang-Mills Theory
We perform the stochastic quantization of Yang-Mills theory in configuration
space and derive the Faddeev-Popov path integral density. Based on a
generalization of the stochastic gauge fixing scheme and its geometrical
interpretation this result is obtained as the exact equilibrium solution of the
associated Fokker--Planck equation. Included in our discussion is the precise
range of validity of our approach.Comment: 19 pages, Late
Generalized Stochastic Gauge Fixing
We propose a generalization of the stochastic gauge fixing procedure for the
stochastic quantization of gauge theories where not only the drift term of the
stochastic process is changed but also the Wiener process itself. All gauge
invariant expectation values remain unchanged. As an explicit example we study
the case of an abelian gauge field coupled with three bosonic matter fields in
0+1 dimensions. We nonperturbatively prove quivalence with the path integral
formalism.Comment: 6 pages, latex, no figure
Nonlinear Phenomena in Canonical Stochastic Quantization
Stochastic quantization provides a connection between quantum field theory
and statistical mechanics, with applications especially in gauge field
theories. Euclidean quantum field theory is viewed as the equilibrium limit of
a statistical system coupled to a thermal reservoir. Nonlinear phenomena in
stochastic quantization arise when employing nonlinear Brownian motion as an
underlying stochastic process. We discuss a novel formulation of the Higgs
mechanism in QED.Comment: 8 pages, invited talk at the International Workshop ``Critical
Phenomena and Diffusion in Complex Systems'', Dec. 5-7, 2006, Nizhni
Novgorod, Russi
Canonical active Brownian motion
Active Brownian motion is the complex motion of active Brownian particles.
They are active in the sense that they can transform their internal energy into
energy of motion and thus create complex motion patterns. Theories of active
Brownian motion so far imposed couplings between the internal energy and the
kinetic energy of the system. We investigate how this idea can be naturally
taken further to include also couplings to the potential energy, which finally
leads to a general theory of canonical dissipative systems. Explicit analytical
and numerical studies are done for the motion of one particle in harmonic
external potentials. Apart from stationary solutions, we study non-equilibrium
dynamics and show the existence of various bifurcation phenomena.Comment: 11 pages, 6 figures, a few remarks and references adde