Investigations In Higher Derivative Field Theories

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.

arXiv commentPhD Thesis; Supervisor: Prof. Rabin Banerjee, Co-Supervisor: Prof. Pradip Mukherjee. Work done at S. N. Bose National Centre for Basic Sciences, Kolkata, India. Degree awarded on 17th Jan, 2015 from the University of Calcutta. arXiv admin note: text overlap with arXiv:1412.3205 by other authors

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