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

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

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.

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

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

Path Integral Formulation of the Conformal Wess-Zumino-Witten to Toda Reductions

The phase space path integral Wess-Zumino-Witten $\to$ Toda reductions are formulated in a manifestly conformally invariant way. For this purpose, the method of Batalin, Fradkin, and Vilkovisky, adapted to conformal field theories, with chiral constraints, on compact two dimensional Riemannian manifolds, is used. It is shown that the zero modes of the Lagrange multipliers produce the Toda potential and the gradients produce the WZW anomaly. This anomaly is crucial for proving the Fradkin-Vilkovisky theorem concerning gauge invariance.Comment: Plain TeX file, 27 page

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

The electromagnetic effects in isospin symmetry breakings of q{\bar q} systems

The isospin symmetry breakings of q{\bar q} are investigated in the QCD sum rule method. The electromagnetic effects are evaluated following the procedure requiring that the electromagnetic effects for charged meson be gauge invariant. We find that the electromagnetic effects are also dominant in the isospin violations of rho meson, which have been shown to be the case in the mass splittings of pions. The numerical results for the difference of pion decay constants and the masses of rho mesons are presented, which are consistent with the data.Comment: To appear in Phys. Rev. D (1997