Unfolded Dynamics Approach and Quantum Field Theory

TL;DR

This paper develops an unfolded dynamics framework for quantizing self-interacting scalar fields, revealing a natural regularization of quantum commutators and connecting 4d quantum field theory with a 5d auxiliary system.

Contribution

It introduces three unfolded formulations of quantum scalar field theory, including a novel regularization of quantum commutators via heat kernels, and links 4d and 5d systems.

Findings

Unfolded quantum commutator is regularized by a heat kernel.

Constructed three related unfolded quantum field theory systems.

Identified a 5d auxiliary system generating 4d scalar action.

Abstract

We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then we systematically construct three different but related unfolded formulations of the corresponding quantum field theory, supporting them with illustrative calculations: an unfolded functional Schwinger-Dyson system, an unfolded system for correlation functions and an unfolded effective system for vertex functions. The most curious feature we reveal is that an unfolded quantum commutator gets naturally regularized: a standard delta-function is replaced with a heat kernel, parameterized by the unfolded proper time. We also identify an auxiliary 5d system, having this proper time as a physical time, which generates 4d scalar action as its on-shell action.