A remark on the Lagrange structure of the unfolded field theory

TL;DR

This paper explores the Lagrange structure of unfolded field theories, demonstrating how the unfolded form affects Lagrangian properties and proposing a method for quantization using the Lagrange anchor, with implications for scalar field theories.

Contribution

It introduces the application of the Lagrange anchor to unfolded field theories, providing a framework for their consistent path-integral quantization.

Findings

Unfolded equations are generally non-Lagrangian despite originating from Lagrangian theories.

The Lagrange anchor can be used to quantize unfolded dynamics.

Unfolded representation of the d'Alembert equation involves infinite derivatives.

Abstract

Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the concept of Lagrange anchor is applied to perform a consistent path-integral quantization of unfolded dynamics. It is shown that the unfolded representation for the canonical Lagrange anchor of the d'Alembert equation inevitably involves an infinite number of space-time derivatives.