Relating spin foams and canonical quantum gravity: (n-1)+1 formulation of nD spin foams

Journal Article · Wed Dec 15 04:00:00 EST 2004 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.70.124004· OSTI ID:20698242

Maran, Suresh K ^[1]

---

1. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)

In this article we lay foundations for a formal relationship of spin foam models of gravity and BF theory to their continuum canonical formulations. First the derivation of the spin foam model of the BF theory from the discrete BF theory action in n dimensions is reviewed briefly. By foliating the underlying n dimensional simplicial manifold using n-1 dimensional simplicial hypersurfaces, the spin foam model is reformulated. Then it is shown that spin network functionals arise naturally on the foliations. The graphs of these spin network functionals are dual to the triangulations of the foliating hypersurfaces. Quantum Transition amplitudes are defined. We calculate the transition amplitudes related to 2D BF theory explicitly. The application to the spin foam models of gravity is discussed briefly.

• OSTI ID: 20698242
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 70; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
COSMOLOGY
FUNCTIONALS
GRAVITATION
QUANTUM GRAVITY
SPIN
TOPOLOGY
TRANSITION AMPLITUDES