65 research outputs found
Covariant Spin Structure
Every Dirac spin structure on a world manifold is associated with a certain
gravitational field, and is not preserved under general covariant
transformations. We construct a composite spinor bundle such that any Dirac
spin structure is its subbundle, and this bundle admits general covariant
transformations.Comment: 26 pages, LaTe
Geometric quantization of mechanical systems with time-dependent parameters
Quantum systems with adiabatic classical parameters are widely studied, e.g.,
in the modern holonomic quantum computation. We here provide complete geometric
quantization of a Hamiltonian system with time-dependent parameters, without
the adiabatic assumption. A Hamiltonian of such a system is affine in the
temporal derivative of parameter functions. This leads to the geometric Berry
factor phenomena.Comment: 20 page
Quantum mechanics with time-dependent parameters
Smooth composite bundles provide the adequate geometric description of
classical mechanics with time-dependent parameters. We show that the Berry's
phase phenomenon is described in terms of connections on composite Hilbert
space bundles.Comment: 7 pages, LaTe
Supermetrics on supermanifolds
By virtue of the well-known theorem, a structure Lie group K of a principal
bundle is reducible to its closed subgroup H iff there exists a global
section of the quotient bundle P/K. In gauge theory, such sections are treated
as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold of
P. Under some conditions, this theorem is extended to principal superbundles in
the category of G-supermanifolds. Given a G-supermanifold M and a graded frame
superbundle over M with a structure general linear supergroup, a reduction of
this structure supergroup to an orthgonal-symplectic supersubgroup is
associated to a supermetric on a G-supermanifold M.Comment: 17 page
Noether's second theorem in a general setting. Reducible gauge theories
We prove Noether's direct and inverse second theorems for Lagrangian systems
on fiber bundles in the case of gauge symmetries depending on derivatives of
dynamic variables of an arbitrary order. The appropriate notions of reducible
gauge symmetries and Noether's identities are formulated, and their equivalence
by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005
Transgression forms and extensions of Chern-Simons gauge theories
A gauge invariant action principle, based on the idea of transgression forms,
is proposed. The action extends the Chern-Simons form by the addition of a
boundary term that makes the action gauge invariant (and not just
quasi-invariant). Interpreting the spacetime manifold as cobordant to another
one, the duplication of gauge fields in spacetime is avoided. The advantages of
this approach are particularly noticeable for the gravitation theory described
by a Chern-Simons lagrangian for the AdS group, in which case the action is
regularized and finite for black hole geometries in diverse situations. Black
hole thermodynamics is correctly reproduced using either a background field
approach or a background-independent setting, even in cases with asymptotically
nontrivial topologies. It is shown that the energy found from the thermodynamic
analysis agrees with the surface integral obtained by direct application of
Noether's theorem.Comment: 28 pages, no figures. Minor changes in the introduction, final
comments and reference
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