by Abhay Ashtekar (Syracuse University) Notes prepared in Collaboration with Ranjeet S Tate

It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.

• Introduction:
  • Non-Perturbative Quantum Gravity: What and Why
  • Overview
• Classical Theory:
  • Lagrangian Framework
  • Legendre Transform: Details
  • From Triads to SU(2) Spinors: A Quick Transition
  • Hamiltonian Formulation
  • Constraint Algebra, Hamiltonians and Dynamics
  • Reality Conditions
  • Inclusion of Matter
• Quantum Theory:
  • The Quantization Program
  • Connection Representation: Linearized Gravity
  • Connection Representation: Issue of Time
  • Connection Representation: CP Problem
  • Loop Representation: Maxwell Theory
  • Loop Representation: Classical Theory
  • Loop Representation: Quantum Theory
  • 2+1 Gravity
• Appendices:
  • Spinors
  • Symplectic Framework
  • Quantum Mechanics on Manifolds
  • Quantization of Constrained Systems
• Bibliography