4,537 research outputs found
Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints
We propose a general method for deformation quantization of any second-class
constrained system on a symplectic manifold. The constraints determining an
arbitrary constraint surface are in general defined only locally and can be
components of a section of a non-trivial vector bundle over the phase-space
manifold. The covariance of the construction with respect to the change of the
constraint basis is provided by introducing a connection in the ``constraint
bundle'', which becomes a key ingredient of the conversion procedure for the
non-scalar constraints. Unlike in the case of scalar second-class constraints,
no Abelian conversion is possible in general. Within the BRST framework, a
systematic procedure is worked out for converting non-scalar second-class
constraints into non-Abelian first-class ones. The BRST-extended system is
quantized, yielding an explicitly covariant quantization of the original
system. An important feature of second-class systems with non-scalar
constraints is that the appropriately generalized Dirac bracket satisfies the
Jacobi identity only on the constraint surface. At the quantum level, this
results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page
Quantum treatment of neutrino in background matter
Motivated by the need of elaboration of the quantum theory of the spin light
of neutrino in matter (), we have studied in more detail the exact
solutions of the Dirac equation for neutrinos moving in the background matter.
These exact neutrino wavefunctions form a basis for a rather powerful method of
investigation of different neutrino processes in matter, which is similar to
the Furry representation of quantum electrodynamics in external fields. Within
this method we also derive the corresponding Dirac equation for an electron
moving in matter and consider the electromagnetic radiation ("spin light of
electron in matter", ) that can be emitted by the electron in this case.Comment: 10 pages, in: Proceedings of QFEXT'05 (The Seventh Workshop on
Quantum Field Theory under the Influence of External Conditions, IEEC, CSIC
and University of Barcelona, Barcelona, Catalonia, Spain, 5-9 September
2005.), ed. by Emilio Elizalde and Sergei Odintsov; published in Journal of
Physics
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