Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity

Open Access
Henderson, Adam Dade
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
August 10, 2011
Committee Members:
  • Abhay Vasant Ashtekar, Dissertation Advisor
  • Abhay Vasant Ashtekar, Committee Chair
  • Paul Sommers, Committee Member
  • Victor Nistor, Committee Member
  • Dezhe Jin, Committee Member
  • Quantum Gravity
  • Path Integral
In this dissertation we present sum of histories formulations of loop quantum cosmology. These are considered for exactly soluble LQC expressed in a Schrodinger form with time provided by a scalar field where we are interested in transition amplitudes and as a constrained system where we are interested in the physical inner product defined by group averaging. As loop quantum cosmology is based on the new quantum mechanics motivated from the representation of loop quantum gravity the sum over histories have many distinct features from standard Feynman path integrals. The sum over histories is given by an discrete sum over histories which change configuration only finitely many times. The resulting sum over histories have strong similarities to the current spin foam models while being derived from a well-controlled canonical quantization. Thus we are able to probe many of the open questions of spin foam models as well as provide new insights and avenues of research.