Canonical quantization of three dimensional gravity in the first order formalism suggests that one should allow singular solutions. This paper addresses the importance of singular solutions in the path integral approach to quantum gravity. Using a simple ansatz for the dreibein and the spin connection in the de-Sitter and the anti-de-Sitter spaces we propose that the sum over the 3D manifolds i...

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the dynamics of the spin and the chirality flips. The problems to overcome in order to find a c-number path integral representation for the solution of the Dirac e...

Recent measurements of the spin-dependent deep inelastic scattering structure functions of the nucleon g p;n 1 (x) are presented. Theoretical diiculties with the traditional separation of the total integral ? p;n of the structure functions into contributions from quark avours is discussed. Techniques using the measurements of semi-inclusive asymmetries that allow direct separation of the avour ...

Abstract. We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric (RS) approximation. A bifurcation analysis of this equation reveals the locations of the ...

We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the “tempo operator”, and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and ...

We consider a simple action for a fractional spin particle and a path integral representation for the propagator is obtained in a gauge such that the constraint embodied in the Lagrangian is not an obstacle. We obtain a propagator for the particle in a constant electromagnetic field via the path integral representation over velocities, which is characterized by arbitrary boundary conditions and...

the synthesis, spectroscopy and magnetic characterization of five new dinuclear copper(ii) complexes are described. all five compounds have the general formula [cu2(l)4(o-r)2](cl)2 or [cu2(l)2(cl)2](cl)2, in which r = ch3 or h, l=2, 3 or 4-pyridinemethanol as l2, l3 or l4, respectively. the title compounds consist of dinuclear units with bridging methoxo groups in [cu2(l4)4(o-ch3)2](cl)2, hydro...

Rigorous derivation of semiclassical approximations in phase space via path integrals [1] for systems with one degree of freedom have recently received considerable attention, both for continuous variables and spin systems. Baranger et al [2], for example, have discussed the canonical coherent state path integral and its semiclassical approximation in some detail, including an initial-value rep...