A massive field-theoretic model for Hodge theory

Abstract

Within the framework of Becchi–Rouet–Stora–Tyutin (BRST) for-malism, we show that the four (3+1)-dimensional (4D)massiveAbelian 2-form gauge theory (without any interaction with mat-terfields)isamodelfortheHodgetheorybecauseitsdiscreteandcontinuoussymmetry transformations (and their correspondingNoether conserved charges) provide the physical realizations ofthe de Rham cohomological operators of differential geometry atthealgebraiclevel. For this purpose, we incorporate thepseudo-scalarandaxial-vectorfields which appear in the theory withnegativekinetic terms (butwith proper definition ofmass). Thenegative kinetic terms, for the above fields, areessentialso thatour theory could respect thediscretesymmetry transformationswhich provide the physical realizations of the Hodge dualityoperation in the domain of differential geometry. Thus, ourpresent endeavour, notonlyprovides the physical realizationsofallthe mathematical ingredients connected with the de Rhamcohomological operators of differential geometry, it also shedslight on the existence and emergence of fields with negativekinetic terms. We discuss the implications and relevance of the latter fields in the context of current models of dark matter anddark energy as well as the bouncing models of Universe.