Square-root actions, metric signature, and the path integral of quantum gravity

Journal Article · Fri Dec 15 04:00:00 EST 1995 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.52.6947· OSTI ID:147838

Carlini, A ^[1]; Greensite, J ^[2]

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1. NORDITA, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
2. Physics and Astronomy Departments, San Francisco State University, San Francisco, California 94117 (United States)

We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ {radical}{ital i} {ital S}] rather than the familiar Feynman expression exp[{ital iS}], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions. {copyright} 1995 The American Physical Society.

• DOE Contract Number: FG03-92ER40711
• OSTI ID: 147838
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 52; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACTION INTEGRAL
CONSTRAINTS
FEYNMAN PATH INTEGRAL
HAMILTONIANS
QUANTIZATION
QUANTUM GRAVITY
UNITARITY