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

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

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

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" $(x^\mu(\tau),p^\mu(\tau))$ 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, $\theta(\tau)$). 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 $Q(D-1,1)\cong U(D-1,1)\ltimes H(D)$, 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 $\theta(\tau)$). 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

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

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

Pathogenesis of Alzheimer's Disease: Molecular and Cellular Mechanisms

peer reviewedAlzheimer's disease is worldwide the leading cause of dementia in the elderly. Senile plaques and neurofibrillary tangles are together with neuronal loss and cortical atrophy characteristic neuropathological features of the disease. Senile plaques contain beta-amyloid (Abeta) peptide which is produced by cleavage of the amyloid precursor protein (APP) by beta- and gamma-secretases. Neurofibrillary tangles are twisted helicoidal strands of hyperphosphorylated tau protein, a microtubule-associated protein. Both pathogenic arms which we describe are interrelated and Abeta deposition seems to potentiate tau pathology. Tangle and plaque formation is influenced by various factors including reciprocal interactions, genetic factors, inflammation and reactive oxygen species. A better understanding of the cellular and molecular cascade which leads to the neuropathological lesions of Alzheimer's disease has led to novel disease-modifying treatment strategies. They yield varying, though encouraging, results and target various stages of the pathological process. Future cooperation between basic, clinical and pharmacological research should allow the development in a foreseeable future of strategies that can halt, or even prevent, this devastating disorder

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

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