Investigations In Higher Derivative Field Theories

TL;DR

This paper develops a systematic approach for analyzing gauge symmetries in higher derivative theories, applying it to particle models, and exploring their connections to W3-algebras and reparametrization invariance.

Contribution

It introduces an extended algorithm for extracting gauge symmetries in higher derivative theories and demonstrates its application to various models, revealing new algebraic structures.

Findings

Connection between gauge symmetry and W3-algebra in relativistic particles

Mapping of gauge symmetry to reparametrization invariance

Application to models in field theory, gravity, and membrane theory

Abstract

Canonical analysis leading to formal quantisation of the higher derivative theories are considered. The first order formalism is adopted where all the configuration space variables along with their higher time derivatives are considered to be independent fields. A systematic algorithm of abstracting the independent gauge symmetries is developed which is an extension of the method developed by Banerjee et al. for the usual first order theories. For the massive relativistic particle model with curvature, we solve the mismatch in the no of independent gauge parameters and no of independent primary fist class constarints. In addition, we show a direct connection between the gauge symmetry and the $W_3$-algebra for the rigid relativistic particle. Also, BRST symmetries for both the massive and massless particle models have been considered and its connection to $W_3$-algebras is demonstrated. The exact mapping of this gauge symmetry is shown with the reparametrisation invariance. Different models from field theory, gravity and membrane theory have been considered as illustrative examples from a new perspective to clarify many not so adequately addressed issues.