Issue |
EPL
Volume 147, Number 3, August 2024
|
|
---|---|---|
Article Number | 32001 | |
Number of page(s) | 7 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ad5f25 | |
Published online | 21 August 2024 |
A 3D field-theoretic example for Hodge theory
1 Department of Physics, Centre of Advanced Studies, Institute of Science, Banaras Hindu University (BHU) Varanasi-221 005, Uttar Pradesh, India
2 DST Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University (BHU) Varanasi-221 005, Uttar Pradesh, India
Received: 15 June 2024
Accepted: 3 July 2024
We focus on the continuous symmetry transformations for the three (2 + 1)-dimensional (3D) system of a combination of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We establish that this combined system is a tractable field-theoretic model of Hodge theory. The symmetry operators of our present system provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. Our present investigation is important in the sense that, for the first time, we are able to establish an odd dimensional (i.e., D = 3) field-theoretic system to be an example for Hodge theory (besides earlier works on a few interesting (0 + 1)-dimensional (1D) toy models as well as a set of well-known SUSY quantum mechanical systems of physical interest). For the sake of brevity, we have purposely not taken into account the 3D Chern-Simon term for the Abelian 1-form gauge field in our theory which allows the mass as well as the gauge invariance to co-exist together.
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