Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Mathematical Physics
2017-06-08 v2 math.MP
Abstract
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.
Keywords
Cite
@article{arxiv.1612.05622,
title = {Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions},
author = {John Haga and Rachel Lash Maitra},
journal= {arXiv preprint arXiv:1612.05622},
year = {2017}
}