Abstract
We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.
Highlights
The formulation based on BRST symmetry [1,2,3,4] plays a crucial role in the discussion of quantization, renormalization, and unitarity and other aspects of gauge theories
We found that the system of particle on a torus is realized as Hodge theory with respect to two different sets of operators
− {Qb, ψ}], where Qb is the BRST charge and ψ is the gauge fixed fermion. This effective action is invariant under BRST transformation generated by Qb which is constructed by using constraints in the theory as
Summary
The formulation based on BRST symmetry [1,2,3,4] plays a crucial role in the discussion of quantization, renormalization, and unitarity and other aspects of gauge theories. On the other hand the charges corresponding to anti-BRST symmetry, anti-dual BRST symmetry, and bosonic symmetry constructed out of these two BRST symmetries are from set of de Rham cohomological operators This indicates that the mathematical foundation of the theory of a particle on a torus is extremely rich. FFBRST is capable of connecting generating functionals of two different effective theories Because of these remarkable properties, FFBRST has become a useful tool of studying various field theoretic systems with BRST symmetry and it has found many applications [30,31,32,33,34,35,36,37,38,39,40,41,42,43].
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