7,345 research outputs found
A Free N = 2 Supersymmetric System: Novel Symmetries
We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric
(SUSY) quantum mechanical system which is the limiting case of a widely-studied
interacting SUSY model of a charged particle constrained to move on a sphere in
the background of a Dirac magnetic monopole. The usual continuous symmetries of
this model provide the physical realization of the de Rham cohomological
operators of differential geometry. The interplay between the novel discrete
symmetries and usual continuous symmetries leads to the physical realization of
relationship between the (co-)exterior derivatives of differential geometry. We
have also exploited the supervariable approach to derive the nilpotent N = 2
SUSY symmetries of the theory and provided the geometrical origin and
interpretation for the nilpotency property. Ultimately, our present study
(based on innate symmetries) proves that our free N = 2 SUSY example is a
tractable model for the Hodge theory.Comment: LaTeX file, 12 pages, Journal reference is give
Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
We derive the complete set of off-shell nilpotent and absolutely
anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST
symmetry transformations for all the fields of the modified version of two
(1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield
formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant
restrictions are exploited together. We capture the (anti-)BRST and
(anti-)co-BRST invariance of the Lagrangian density in the language of
superfield formalism. We also express the nilpotency and absolute
anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the
framework of augmented superfield formalism. This exercise leads to some novel
observations which have, hitherto, not been pointed out in the literature
within the framework of superfield approach to BRST formalism. For the sake of
completeness, we also mention, very briefly, a unique bosonic symmetry, the
ghost-scale symmetry and discrete symmetries of the theory and show that the
algebra of conserved charges captures the cohomological aspects of differential
geometry. Thus, our present modified 2D Proca theory is a model for the Hodge
Theory.Comment: LaTeX file, 32 pages, journal reference give
- …