On the Continuum Limit of Curvature Squared Actions in the Regge Calculus

Eliezer, D.

doi:10.1016/0550-3213(89)90623-8

On the Continuum Limit of Curvature Squared Actions in the Regge Calculus

1989

20 pages

Published in:

Nucl.Phys.B 319 (1989) 667-686

Published: 1989

DOI:

10.1016/0550-3213(89)90623-8

View in:

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Abstract: (Elsevier)

We evaluate the continuum limit of a family of curvature squared actions for the Regge calculus proposed by Hamber and Williams. The answers depend on how the continuum limit is defined. When the link lengths are defined as the distance in an embedding space between the endpoints of the link, we find that no member of this family approaches the continuum limit correctly. Defining the link lenghts as the length of a geodesic between the endpoints of the link, we find that a unique member is selected, and we prove for the general two dimensional compact manifold that this Regge calculus action converges to ∫ R 2 √ g d 2 x .

LATTICE FIELD THEORY: REGGE
LATTICE FIELD THEORY: ACTION
LATTICE FIELD THEORY: CONTINUUM LIMIT
QUANTUM GRAVITY

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