240 research outputs found
On the emergence of gauge structures and generalized spin when quantizing on a coset space
It has been known for some time that there are many inequivalent
quantizations possible when the configuration space of a system is a coset
space G/H. Viewing this classical system as a constrained system on the group
G, we show that these inequivalent quantizations can be recovered from a
generalization of Dirac's approach to the quantization of such a constrained
system within which the classical first class constraints (generating the
H-action on G) are allowed to become anomalous (second class) when quantizing.
The resulting quantum theories are characterized by the emergence of a
Yang-Mills connection, with quantized couplings, and new 'spin' degrees of
{}freedom. Various applications of this procedure are presented in detail:
including a new account of how spin can be described within a path-integral
formalism, and how on S^4 chiral spin degrees of {}freedom emerge, coupled to a
BPST instanton.Comment: 64 pages, plain TeX, DIAS-STP-93-1
When photons are lying about where they have been
The past of the photon in a nested Mach-Zehnder interferometer with an
inserted Dove prism is analyzed. It is argued that the Dove prism does not
change the past of the photon. Alonso and Jordan correctly point out that an
experiment by Danan et al. demonstrating the past of the photon in nested
interferometer will show different results when the Dove prism is inserted. The
reason, however, is not that the past is changed, but that the experimental
demonstration becomes incorrect. The explanation of a signal from the place in
which the photon was (almost) not present is given. Bohmian trajectory of the
photon is specified.Comment: 6 pages, 3 figures; revised and expanded versio
Induced Gauge Fields in the Path Integral
The path integral on a homogeneous space is constructed, based on the
guiding principle `first lift to and then project to '. It is then
shown that this principle admits inequivalent quantizations inducing a gauge
field (the canonical connection) on the homogeneous space, and thereby
reproduces the result obtained earlier by algebraic approaches.Comment: 12 pages, no figures, LaTe
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