46,356 research outputs found
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, , 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, , 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
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