Comments on Good's Proposal for New Rules of Quantization

In a recent paper \cite{[Good1]} Good postulated new rules of quantization, one of the major features of which is that the quantum evolution of the wave function is always given by ordinary differential equations. In this paper we analyse the proposal in some detail and discuss its viability and its relationship with the standard quantum theory. As a byproduct, a simple derivation of the `mass spectrum' for the Klein-Gordon field is presented, but it is also shown that there is a complete additional spectrum of negative `masses'. Finally, two major reasons are presented against the viability of this alternative proposal: a) It does not lead to the correct energy spectrum for the hydrogen atom. b) For field models, the standard quantum theory cannot be recovered from this alternative description.Comment: Minor corrections have been made. To appear in J.Math.Phy

Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, particularly to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyse, in a systematic manner and with complete generality, the case of linear fields (abelian current groups). To ilustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the abelian Chern-Simons models over an arbitrary closed surface in detail.Comment: Plain LaTeX, 31 pages, no macros. To appear in J. Math. Phy

The Electromagnetic and Proca Fields Revisited: a Unified Quantization

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, $A_{\mu}(x)\rightarrow A_{\mu}(x)+\partial_{\mu}\varphi(x)$, into a group law. In this paper it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, $U(1)(\vec{x},t)$, acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.Comment: 16 pages, latex, no figure