Quantum effective action in spacetimes with branes and boundaries
Abstract
We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested NeumannDirichlet duality which we extend beyond the treelevel approximation. In the oneloop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the branethe inverse of the branetobrane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent wellknown difficulties in the heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowestorder surface terms in the case of Robin and oblique boundary onditions. We briefly discuss multiloop applications of the suggested Dirichlet reduction and the prospects of constructing the universal backgroundfield method for systems with branes/boundaries, analogous to the SchwingerDeWitt technique.
 Authors:
 Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 20782711
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.066012; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; APPROXIMATIONS; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; DUALITY; MEMBRANES; PROPAGATOR; QUANTUM GRAVITY; SPACETIME; SURFACES
Citation Formats
Barvinsky, A.O., and Nesterov, D.V. Quantum effective action in spacetimes with branes and boundaries. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.066012.
Barvinsky, A.O., & Nesterov, D.V. Quantum effective action in spacetimes with branes and boundaries. United States. doi:10.1103/PHYSREVD.73.066012.
Barvinsky, A.O., and Nesterov, D.V. Wed .
"Quantum effective action in spacetimes with branes and boundaries". United States.
doi:10.1103/PHYSREVD.73.066012.
@article{osti_20782711,
title = {Quantum effective action in spacetimes with branes and boundaries},
author = {Barvinsky, A.O. and Nesterov, D.V.},
abstractNote = {We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested NeumannDirichlet duality which we extend beyond the treelevel approximation. In the oneloop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the branethe inverse of the branetobrane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent wellknown difficulties in the heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowestorder surface terms in the case of Robin and oblique boundary onditions. We briefly discuss multiloop applications of the suggested Dirichlet reduction and the prospects of constructing the universal backgroundfield method for systems with branes/boundaries, analogous to the SchwingerDeWitt technique.},
doi = {10.1103/PHYSREVD.73.066012},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}

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