1,334 research outputs found
Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector
The quantisation of gauge invariant systems usually proceeds through some
gauge fixing procedure of one type or another. Typically for most cases, such
gauge fixings are plagued by Gribov ambiguities, while it is only for an
admissible gauge fixing that the correct dynamical description of the system is
represented, especially with regards to non perturbative phenomena. However,
any gauge fixing procedure whatsoever may be avoided altogether, by using
rather a recently proposed new approach based on the projection operator onto
physical gauge invariant states only, which is necessarily free on any such
issues. These different aspects of gauge invariant systems are explicitely
analysed within a solvable U(1) gauge invariant quantum mechanical model
related to the dimensional reduction of Yang-Mills theory.Comment: 22 pages, no figures, plain LaTeX fil
Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings
It is shown that background fields of a topological character usually
introduced as such in compactified string theories correspond to quantum
degrees of freedom which parametrise the freedom in choosing a representation
of the zero mode quantum algebra in the presence of non-trivial topology. One
consequence would appear to be that the values of such quantum degrees of
freedom, in other words of the associated topological background fields, cannot
be determined by the nonperturbative string dynamics.Comment: 1+10 pages, no figure
Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation
There exists a well-known duality between the Maxwell-Chern-Simons theory and
the self-dual massive model in 2+1 dimensions. This dual description has been
extended to topologically massive gauge theories (TMGT) in any dimension. This
Letter introduces an unconventional approach to the construction of this type
of duality through a reparametrisation of the master theory action. The dual
action thereby obtained preserves the same gauge symmetry structure as the
original theory. Furthermore, the dual action is factorised into a propagating
sector of massive gauge invariant variables and a sector with gauge variant
variables defining a pure topological field theory. Combining results obtained
within the Lagrangian and Hamiltonian formulations, a new completed structure
for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure
Nonabelian Global Chiral Symmetry Realisation in the Two-Dimensional N Flavour Massless Schwinger Model
The nonabelian global chiral symmetries of the two-dimensional N flavour
massless Schwinger model are realised through bosonisation and a vertex
operator construction.Comment: To appear in the Proceedings of the Fourth International Workshop on
Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou
(Republic of Benin) (World Scientific, Singapore, 2006), 1+7 pages, no
figure
The Physical Projector and Topological Quantum Field Theories: U(1) Chern-Simons Theory in 2+1 Dimensions
The recently proposed physical projector approach to the quantisation of
gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1
dimensions as one of the simplest examples of a topological quantum field
theory. The physical projector is explicitely demonstrated to be capable of
effecting the required projection from the initially infinite number of degrees
of freedom to the finite set of gauge invariant physical states whose
properties are determined by the topology of the underlying manifold.Comment: 24 pages, no figures, plain LaTeX file; one more reference added.
Final version to appear in Jour. Phys.
Bosonization of the Schwinger Model by Noncommutative Chiral Bosons
Bosonization of the Schwinger model with noncommutative chiral bosons is
considered on a spacetime of cylinder topology. Using point splitting
regularization, manifest gauge invariance is maintained throughout. Physical
consequences are discussed.Comment: To appear in the Proceedings of the Fourth International Workshop on
Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou
(Republic of Benin) (World Scientific, Singapore, 2006), 1+8 pages, no
figure
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
Gauge Invariant Factorisation and Canonical Quantisation of Topologically Massive Gauge Theories in Any Dimension
Abelian topologically massive gauge theories (TMGT) provide a topological
mechanism to generate mass for a bosonic p-tensor field in any spacetime
dimension. These theories include the 2+1 dimensional Maxwell-Chern-Simons and
3+1 dimensional Cremmer-Scherk actions as particular cases. Within the
Hamiltonian formulation, the embedded topological field theory (TFT) sector
related to the topological mass term is not manifest in the original phase
space. However through an appropriate canonical transformation, a gauge
invariant factorisation of phase space into two orthogonal sectors is feasible.
The first of these sectors includes canonically conjugate gauge invariant
variables with free massive excitations. The second sector, which decouples
from the total Hamiltonian, is equivalent to the phase space description of the
associated non dynamical pure TFT. Within canonical quantisation, a likewise
factorisation of quantum states thus arises for the full spectrum of TMGT in
any dimension. This new factorisation scheme also enables a definition of the
usual projection from TMGT onto topological quantum field theories in a most
natural and transparent way. None of these results rely on any gauge fixing
procedure whatsoever.Comment: 1+25 pages, no figure
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