1,106 research outputs found
Solving Gauge Invariant Systems without Gauge Fixing: the Physical Projector in 0+1 Dimensional Theories
The projector onto gauge invariant physical states was recently constructed
for arbitrary constrained systems. This approach, which does not require gauge
fixing nor any additional degrees of freedom beyond the original ones---two
characteristic features of all other available methods for quantising
constrained dynamics---is put to work in the context of a general class of
quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge
groups are considered specifically, and a comprehensive understanding of the
corresponding physical spectra is achieved in a straightforward manner, using
only standard methods of coherent states and group theory which are directly
amenable to generalisation to other Lie algebras. Results extend by far the few
examples available in the literature from much more subtle and delicate
analyses implying gauge fixing and the characterization of modular space.Comment: 32 pages, LaTeX fil
On Electric Fields in Low Temperature Superconductors
The manifestly Lorentz covariant Landau-Ginzburg equations coupled to
Maxwell's equations are considered as a possible framework for the effective
description of the interactions between low temperature superconductors and
magnetic as well as electric fields. A specific experimental set-up, involving
a nanoscopic superconductor and only static applied fields whose geometry is
crucial however, is described, which should allow to confirm or invalidate the
covariant model through the determination of the temperature dependency of the
critical magnetic-electric field phase diagram and the identification of some
distinctive features it should display.Comment: 14 pages (Latex) + 2 postscript figure
The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane
The N=1 supersymmetric invariant Landau problem is constructed and solved. By
considering Landau level projections remaining non trivial under N=1
supersymmetry transformations, the algebraic structures of the N=1
supersymmetric covariant non(anti)commutative superplane analogue of the
ordinary N=0 noncommutative Moyal-Voros plane are identified
Gauge Fixing and BFV Quantization
Nonsingularity conditions are established for the BFV gauge-fixing fermion
which are sufficient for it to lead to the correct path integral for a theory
with constraints canonically quantized in the BFV approach. The conditions
ensure that anticommutator of this fermion with the BRST charge regularises the
path integral by regularising the trace over non-physical states in each ghost
sector. The results are applied to the quantization of a system which has a
Gribov problem, using a non-standard form of the gauge-fixing fermion.Comment: 14 page
Computation of normal form coefficients of cycle bifurcations of maps by algorithmic differentiation
Coordinate-free quantization of first-class constrained systems
The coordinate-free formulation of canonical quantization, achieved by a
flat-space Brownian motion regularization of phase-space path integrals, is
extended to a special class of closed first-class constrained systems that is
broad enough to include Yang-Mills type theories with an arbitrary compact
gauge group. Central to this extension are the use of coherent state path
integrals and of Lagrange multiplier integrations that engender projection
operators onto the subspace of gauge invariant states
Coherent State Quantization of Constraint Systems
A careful reexamination of the quantization of systems with first- and
second-class constraints from the point of view of coherent-state phase-space
path integration reveals several significant distinctions from more
conventional treatments. Most significantly, we emphasize the importance of
using path-integral measures for Lagrange multipliers which ensure that the
quantum system satisfies the quantum constraint conditions. Our procedures
involve no delta-functionals of the classical constraints, no need for gauge
fixing of first-class constraints, no need to eliminate second-class
constraints, no potentially ambiguous determinants, and have the virtue of
resolving differences between canonical and path-integral approaches. Several
examples are considered in detail.Comment: Latex, 38 pages, no figure
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