849 research outputs found
Revisiting the Fradkin-Vilkovisky Theorem
The status of the usual statement of the Fradkin-Vilkovisky theorem, claiming
complete independence of the Batalin-Fradkin-Vilkovisky path integral on the
gauge fixing "fermion" even within a nonperturbative context, is critically
reassessed. Basic, but subtle reasons why this statement cannot apply as such
in a nonperturbative quantisation of gauge invariant theories are clearly
identified. A criterion for admissibility within a general class of gauge
fixing conditions is provided for a large ensemble of simple gauge invariant
systems. This criterion confirms the conclusions of previous counter-examples
to the usual statement of the Fradkin-Vilkovisky theorem.Comment: 21 pages, no figures, to appear in Jnl. Phys.
The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations
In order to assess possible observable effects of noncommutativity in
deformations of quantum mechanics, all irreducible representations of the
noncommutative Heisenberg algebra and Weyl-Heisenberg group on the two-torus
are constructed. This analysis extends the well known situation for the
noncommutative torus based on the algebra of the noncommuting position
operators only. When considering the dynamics of a free particle for any of the
identified representations, no observable effect of noncommutativity is
implied.Comment: 24 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
World-line Quantisation of a Reciprocally Invariant System
We present the world-line quantisation of a system invariant under the
symmetries of reciprocal relativity (pseudo-unitary transformations on ``phase
space coordinates" which preserve the Minkowski
metric and the symplectic form, and global shifts in these coordinates,
together with coordinate dependent transformations of an additional compact
phase coordinate, ). The action is that of free motion over the
corresponding Weyl-Heisenberg group. Imposition of the first class constraint,
the generator of local time reparametrisations, on physical states enforces
identification of the world-line cosmological constant with a fixed value of
the quadratic Casimir of the quaplectic symmetry group , the semi-direct product of the pseudo-unitary group with
the Weyl-Heisenberg group (the central extension of the global translation
group, with central extension associated to the phase variable ).
The spacetime spectrum of physical states is identified. Even though for an
appropriate range of values the restriction enforced by the cosmological
constant projects out negative norm states from the physical spectrum, leaving
over spin zero states only, the mass-squared spectrum is continuous over the
entire real line and thus includes a tachyonic branch as well
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
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.
Spectrum of the non-commutative spherical well
We give precise meaning to piecewise constant potentials in non-commutative
quantum mechanics. In particular we discuss the infinite and finite
non-commutative spherical well in two dimensions. Using this, bound-states and
scattering can be discussed unambiguously. Here we focus on the infinite well
and solve for the eigenvalues and eigenfunctions. We find that time reversal
symmetry is broken by the non-commutativity. We show that in the commutative
and thermodynamic limits the eigenstates and eigenfunctions of the commutative
spherical well are recovered and time reversal symmetry is restored
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
Thermodynamics of a non-commutative fermion gas
Building on the recent solution for the spectrum of the non-commutative well
in two dimensions, the thermodynamics that follows from it is computed. In
particular the focus is put on an ideal fermion gas confined to such a well. At
low densities the thermodynamics is the same as for the commutative gas.
However, at high densities the thermodynamics deviate strongly from the
commutative gas due to the implied excluded area resulting from the
non-commutativity. In particular there are extremal macroscopic states,
characterized by area, number of particles and angular momentum, that
correspond to a single microscopic state and thus have vanishing entropy. When
the system size and excluded area are comparable, thermodynamic quantities,
such as entropy, exhibit non-extensive features.Comment: 18 pages, 11 figure
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