The role of BRST charge as a generator of gauge transformations in quantization of gauge theories and Gravity

Abstract

Department of Theoretical and Computational Physics, Southern Federal University,Ul. Sorge, 5, Rostov-on-Don 344090, Russia.E-mail: shestakova@sfedu.ruIn the Batalin-Fradkin-Vilkovisky approach to quantization of gauge theories a principal role is given to the BRST chargewhich can be constructed as a series in Grassmannian (ghost) variables with coecients given by generalized structurefunctions of constraints algebra. Alternatively, the BRST charge can be derived making use of the Noether theorem andglobal BRST invariance of the e ective action. In the case of Yang-Mills elds the both methods lead to the same expressionfor the BRST charge, but it is not valid in the case of General Relativity. It is illustrated by examples of an isotropiccosmological model as well as by spherically-symmetric gravitational model which imitates the full theory of gravity muchbetter. The consideration is based on Hamiltonian formulation of General Relativity in extended phase space. At thequantum level the structure of the BRST charge is of great importance since BRST invariant quantum states are believedto be physical states. Thus, the de nition of the BRST charge at the classical level is inseparably related to our attemptsto nd a true way to quantize gravity.Keywords: BRST charge, gauge transformations, Noether theorem, physical states, quantization of gravity.