Alladi Ramakrishnan Hall

BRST, anti-BRST and Dark Objects

R. P. Malik

Banares Hindu University

Tracing the importance of gauge theories, their quantization problems and importance of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we shall lay emphasis on the existence of Curci-Ferrrai (CF) type restrictions in the context of a complete description of quantum gauge theories.We shall establish that the Stuckelberg modified versions of 2D Proca and 2D massive Abelian 2-form gauge theories are the models for Hodge theory whose discrete and continuous symmetry transformations provide the physical realisations of the de Rham cohomological operators of differential geometry within the framework of BRST formalism. We shall demonstrate that, in this proof, we are forced to incorporate fields with
negative kinetic terms on the firm ground of symmetries. These extra fields possess properly defined mass. As a consequence, such objects are the candidates of dark matter and, the massless limit of the above 2D proca and 4D massive Abelian 2-form gauge theories, require only fields with negative kinetic terms which turn out to be the candidates for dark energy. Thus, we provide a unified theoretical framework for the existence of dark matter and dark energy within the framework of QFT.

Tracing the importance of gauge theories, their quantization problems and importance of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we shall lay emphasis on the existence of Curci-Ferrrai (CF) type restrictions in the context of a complete description of quantum gauge theories.We shall establish that the Stuckelberg modified versions of 2D Proca and 2D massive Abelian 2-form gauge theories are the models for Hodge theory whose discrete and continuous symmetry transformations provide the physical realisations of the de Rham cohomological operators of differential geometry within the framework of BRST formalism. We shall demonstrate that, in this proof, we are forced to incorporate fields with
negative kinetic terms on the firm ground of symmetries. These extra fields possess properly defined mass. As a consequence, such objects are the candidates of dark matter and, the massless limit of the above 2D proca and 4D massive Abelian 2-form gauge theories, require only fields with negative kinetic terms which turn out to be the candidates for dark energy. Thus, we provide a unified theoretical framework for the existence of dark matter and dark energy within the framework of QFT.