Speaker: Dr. Suresh K Maran
Title: Classical and Spin Foam Quantum Gravity for Complex, Real Orthogonal Groups and the Square of Area Reality Constraint
Abstract: Complex general relativity is the analytical continuation of the SO(4,C) general relativity on a real 4D manifold to a complex 4D manifold. By modifying the Plebanski theory of the SO(4,C)general relativity by adding a Lagrange multiplier to impose the area metric reality condition, the classical real general relativity theories for all signatures can be derived. Spin foams are path integral quantizations of discrete general relativity on simplicial manifolds. Various spin foam models for general relativity are available, the most popular being the Barrett-Crane models. The discrete form of the area metric on a simplicial manifold is the square of areas of the 2-simplices. In spin foams the Casimir values of the representations that are used to label the 2-simplices are defined as the square of the areas. The discretized SO(4,C) general relativity cannot be analytically continued to complex general relativity but it can be spin foam quantized. First I discuss the derivation of the Barrett-Crane model for SO(4,C) general relativity using a new direct procedure. Then by imposing the square of area reality condition the spin foams of real general relativity for all 4D signatures can be formally deduced in an intuitive way. By this procedure the Barrett-Crane models for all 4D signatures and the SO(4,C) general relativity are unified under a general picture. If time is available I will discuss the following ideas briefly: Relating spin foams to the spin network functionals of canonical quantum general relativity, the asymptotic limit of spin foams and the SO(4,C) Regge Calculus as a general form of Regge Calculus in 4D.
Talk: Transparencies, Recorded Talk