# Novel symmetries in the modified version of two dimensional Proca theory

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## Abstract

By exploiting Stueckelberg’s approach, we obtain a gauge theory for the two-dimensional, that is, (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the *usual* Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the *total* gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a *unique* bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.

## Keywords

Lagrangian Density Symmetry Transformation Ghost Number Hodge Theory Hodge Duality## Notes

### Acknowledgements

Discussion with R. Kumar, in the initial stages of our present investigation, is thankfully acknowledged. T.B. is grateful to BHU-fellowship and D.S. thanks UGC, Government of India, New Delhi, for financial support through RFSMS scheme, under which the present investigation has been carried out.

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