Regge calculus and Ashtekar variables

Abstract

Spacetime discretized in simplexes, as proposed in the pioneer work of Regge, is described in terms of selfdual variables. In particular, we elucidate the "kinematic" structure of the initial value problem, in which 3--space is divided into flat tetrahedra, paying particular attention to the role played by the reality condition for the Ashtekar variables. An attempt is made to write down the vector and scalar constraints of the theory in a simple and potentially useful way.

10 pages, uses harvmac. DFUPG 83/94

References in corpus (2)

• Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
• The reality conditions for the new canonical variables of General Relativity

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• Quantizing Regge calculus
• Exact Bianchi Identity in Regge Gravity
• An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
• Note on $SU(2)$ isolated horizon