BRST and Related Superfield Approach to a Few Interesting Models of Point Particles and a Model of Bosonic String: A Brief Review

Abstract

In this brief review-cum-research article, we discuss a few key aspects of the off-shell nilpotent (anti-)BRST symmetry transformations, Curci-Ferrari (CF) type restriction(s), coupled Lagrangians/Lagrangian densities, etc., for the 1D diffeomorphism (i.e. reparameterization) invariant models of $(i)$ a non-relativistic and non-SUSY free particle, $(ii)$ a scalar (i.e. non-SUSY) relativistic free particle, $(iii)$ a spinning (i.e. SUSY) relativistic free particle, and $(iv)$ a 2D diffeomorphism invariant model of a specific bosonic string theory within the framework of BRST and related supervariable/superfield approach. We take up a new 1D diffeomorphism invariant model of an interacting scalar relativistic particle with the electromagnetic field. The latter is treated as a constant background variable and is, therefore, independent of the evolution parameter. We show that the universal nature of the CF-type restriction is maintained in the case of this new model, too. We exploit the modified Bonora-Tonin supervariable/superfield approach (MBTSA) to BRST formalism in the context of the 1D and 2D diffeomorphism invariant theories to prove the universal nature of the CF-type restriction(s). We further demonstrate that the 1D diffeomorphism invariant models of all kinds of particles are described by the singular Lagrangians. This singular nature has, to the best of our knowledge, not been explicitly shown elsewhere. Thus, these 1D models also respect the gauge symmetry transformations which are generated by the first-class constraints that exist on them. The equivalence of the 1D diffeomorphism and gauge symmetries is also established under specific conditions..

arXiv commentLaTeX file, 45 pages, minor typos fixed, journal reference given

References in corpus (16)

• Time of occurrence observable in quantum mechanics
• New topological field theories in two dimensions
• BRST, anti-BRST and gerbes
• BRST, anti-BRST and their geometry
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• Proper BRST quantization of relativistic particles
• Comments on BRST quantization of strings
• General Procedure of Gauge Fixings and Ghosts
• Noncommutativity and Reparametrisation symmetry
• Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism
• Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle
• BRST Field Theory of Relativistic Particles
• 1D Diffeomorphism Invariant Model of a Free Scalar Relativistic Particle: Supervariable and BRST Approaches
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Superfield Approaches to a Model of Bosonic String: Curci-Ferrari Type Restrictions