Some remarks on singularities in quantum cosmology

We discuss to what extent classical singularities persist upon quantization in two simple cosmological models.Comment: 4 pps., LaTeX2e. Substantial revisions. To appear in: Proc. of the Second Conference on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 September 1996. Edited by V. de Alfaro et a

On a Full Quantization of the Torus

I exhibit a prequantization of the torus which is actually a ``full'' quantization in the sense that a certain complete set of classical observables is irreducibly represented. Thus in this instance there is no Groenewold-Van Hove obstruction to quantization.Comment: 8 pages, AMS-LaTe

Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T ^μ _ν that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor T ^μ _ν is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the “correction terms” that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our T^(μν) coincides with the Hilbert tensor and hence is automatically symmetric

Finite dimesional Hamiltonian formalism for gauge and field theories

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized Poisson $\mathfrak{p}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field.Comment: 52 pages. In this paper we give a more general hamiltonian formulation for a gauge and field theories, it's an extension of our previous paper math-ph/000402

Precanonical Quantization and the Schroedinger Wave Functional

A relation between the Schroedinger wave functional and the Clifford-valued wave function which appears in what we call precanonical quantization of fields and fulfills a Dirac-like generalized covariant Schroedinger equation on the space of field and space-time variables is discussed. The Schroedinger wave functional is argued to be the trace of the positive frequency part of the continual product over all spatial points of the values of the aforementioned wave function restricted to a Cauchy surface. The standard functional differential Schroedinger equation is derived as a consequence of the Dirac-like covariant Schroedinger equation.Comment: 16pp, LaTeX2e. v2: minor changes in the presentation, misprints in eqs. 4.21, 4.24 and unnumbered after eq. 4.8 fixed, sect. 4.1 partly rewritten, the conclusions section expanded, references added, LaTeX format changed; to appear in Phys. Lett.