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 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

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

The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem

A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.Comment: 10 page

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

Hybrid States from Constituent Glue Model

The hybrid meson is one of the most interesting new hadron specie beyond the naive quark model. It acquire a great attention both from the theoretical and experimental efforts. Many good candidates have been claimed to be observed, but there is no absolute confirmation about existence of hybrid mesons. In the present work we propose new calculations of the masses and decay widths of the hybrid mesons in the context of constituent gluon model.Comment: 19 pages, 11 Table

Predicted electric field near small superconducting ellipsoids

We predict the existence of large electric fields near the surface of superconducting bodies of ellipsoidal shape of dimensions comparable to the penetration depth. The electric field is quadrupolar in nature with significant corrections from higher order multipoles. Prolate (oblate) superconducting ellipsoids are predicted to exhibit fields consistent with negative (positive) quadrupole moments, reflecting the fundamental charge asymmetry of matter.Comment: To be published in Phys.Rev.Let

Finite Euler Hierarchies And Integrable Universal Equations

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, {\it classical\ts} topological field theories -- whose classical solutions span topological classes of manifolds -- and reparametrisation invariant theories -- generalising ordinary string and membrane theories. On the other hand, {\it finite} Euler hierarchies are constructed for all three classes of theories. These hierarchies terminate with {\it universal\ts} equations of motion, probably defining new integrable systems as they admit an infinity of Lagrangians. Speculations as to the possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p., (Plain TeX), DTP-92/3

Bound state energies and phase shifts of a non-commutative well

Non-commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non-commutative configuration space. Within this framework an unambiguous definition can be given for the non-commutative well. Using this approach we compute the bound state energies, phase shifts and scattering cross sections of the non- commutative well. As expected the results are very close to the commutative results when the well is large or the non-commutative parameter is small. However, the convergence is not uniform and phase shifts at certain energies exhibit a much stronger then expected dependence on the non-commutative parameter even at small values.Comment: 12 pages, 8 figure