1,517 research outputs found
Zero modes, gauge fixing, monodromies, -functions and all that
We discuss various issues associated with the calculation of the reduced
functional determinant of a special second order differential operator
\boldmath{F}, , with a
generic function , subject to periodic and Dirichlet boundary
conditions. These issues include the gauge-fixed path integral representation
of this determinant, the monodromy method of its calculation and the
combination of the heat kernel and zeta-function technique for the derivation
of its period dependence. Motivations for this particular problem, coming from
applications in quantum cosmology, are also briefly discussed. They include the
problem of microcanonical initial conditions in cosmology driven by a conformal
field theory, cosmological constant and cosmic microwave background problems.Comment: 17 pages, to appear in J. Phys. A: Math. Theor. arXiv admin note:
substantial text overlap with arXiv:1111.447
Unimodular Gravity in Restricted Gauge Theory Setup
We develop Lagrangian quantization formalism for a class of theories obtained
by the restriction of the configuration space of gauge fields from a wider
(parental) gauge theory. This formalism is based on application of
Batalin-Vilkovisky technique for quantization of theories with linearly
dependent generators, their linear dependence originating from a special type
of projection from the originally irreducible gauge generators of the parental
theory. The algebra of these projected generators is shown to be closed for
parental gauge algebras closed off shell. We demonstrate that new physics of
the restricted theory as compared to its parental theory is associated with the
rank deficiency of a special gauge restriction operator reflecting the gauge
transformation properties of the restriction constraints functions -- this
distinguishes restriction of the theory from its partial gauge fixing. As a
byproduct of this technique a workable algorithm for one-loop effective action
in generic first-stage reducible theory was constructed, along with the
explicit set of tree-level Ward identities for gauge field, ghost and
ghosts-for-ghosts propagators, which guarantee on-shell gauge independence of
this effective action. The restricted theory formalism with reducible set of
projected gauge generators is applied to unimodular gravity theory by using
background-covariant gauge-fixing procedure. Its one-loop effective action is
obtained in terms of functional determinants of minimal second order
differential operators calculable on generic backgrounds by Schwinger-DeWitt
technique of local curvature expansion. The result is shown to be equivalent to
Einstein gravity theory with a cosmological term up to a special contribution
of the global degree of freedom associated with the variable value of the
cosmological constant. The role of this degree of freedom is briefly discussed.Comment: 47 page
Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity
A new quasigroup approach to conservation laws in general relativity is
applied to study asymptotically flat at future null infinity spacetime. The
infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to
the Poincar\'e quasigroup and the Noether charge associated with any element of
the Poincar\'e quasialgebra is defined. The integral conserved quantities of
energy-momentum and angular momentum are linear on generators of Poincar\'e
quasigroup, free of the supertranslation ambiguity, posess the flux and
identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page
Heat kernel methods for Lifshitz theories
We study the one-loop covariant effective action of Lifshitz theories using
the heat kernel technique. The characteristic feature of Lifshitz theories is
an anisotropic scaling between space and time. This is enforced by the
existence of a preferred foliation of space-time, which breaks Lorentz
invariance. In contrast to the relativistic case, covariant Lifshitz theories
are only invariant under diffeomorphisms preserving the foliation structure. We
develop a systematic method to reduce the calculation of the effective action
for a generic Lifshitz operator to an algorithm acting on known results for
relativistic operators. In addition, we present techniques that drastically
simplify the calculation for operators with special properties. We demonstrate
the efficiency of these methods by explicit applications.Comment: 36 pages, matches journal versio
Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles
A nonassociative generalization of the principal fiber bundles with a smooth
loop mapping on the fiber is presented. Our approach allows us to construct a
new kind of gauge theories that involve higher ''nonassociative'' symmetries.Comment: 20 page
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