Perturbative quantum cosmology around the [ital scrMscrS]([ital T][sup [ital d]]) minisuperspace

Journal Article · Mon Feb 15 04:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1391· OSTI ID:6993735

Peleg, Y ^[1]

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1. Physics Department, Technion-Israel Institute of Technology, Haifa 32000 (Israel)

We study the Wheeler-DeWitt equation for the cases of first- and second-order perturbations around the [ital scrMscrS]([ital T][sup [ital d]]) minisuperspace, which is the Wheeler superspace of all flat and orthogonal tori in [ital d] dimensions. To first order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic massless Klein-Gordon equation. A definition of a Hilbert space in that region of superspace is straightforward, but the dynamics is trivial. To second order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic Klein-Gordon equation, but with a mass-squared term which is time dependent. This time dependence ruins the possibility of a simple definition of a Hilbert space.

• OSTI ID: 6993735
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:4; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
BOUNDARY CONDITIONS
COSMOLOGY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
HILBERT SPACE
KLEIN-GORDON EQUATION
LAGRANGIAN FUNCTION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
SPACE-TIME
SUPERSYMMETRY
SYMMETRY
TIME DEPENDENCE
WAVE EQUATIONS