Path Integral representation for Polymer Quantized Scalar Fields

Abstract

According to loop quantum gravity, matter fields must be quantized in a background independent manner. For scalar fields, such a background independent quantization is called polymer quantization and is inequivalent to the standard Schrodinger quantization. It is therefore important to obtain predictions from the polymer quantized scalar field theory and compare with the standard results. As a step towards this, we develop a path integral representation for the polymer quantized scalar field. We notice several crucial differences from the path integral for the schrodinger quantized scalar field. One important difference is the appearance of an extra summation at each point in the path integral for the polymer quantized theory. A second crucial difference is the loss of manifest Lorentz symmetry for a polymer quantized theory on Minkowski Space.

In this version, the derivation of the path integral is presented starting from the position basis instead of the momentum basis to better highlight the similarities with particle on a circle

References in corpus (4)

• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• The propagator in polymer quantum field theory
• Polymer quantization and Symmetries
• On obtaining classical mechanics from quantum mechanics

Cited by in corpus (6)

• Path integral polymer propagator of relativistic and non-relativistic particles
• Polymer Quantization predicts radiation in inertial frames
• Bounds on the Polymer Scale from Gamma Ray Bursts
• How is Lorentz Invariance encoded in the Hamiltonian?
• Dimensional Phenomenology in Polymeric Quantization Framework
• Low Energy Consequences of Loop Quantum Gravity