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BRST Charge and Poisson Algebras

Abstract : An elementary introduction to the classical version of gauge theories is made. The shortcomings of the usual gauge fixing process are pointed out. They justify the need to replace it by a global symmetry: the BRST symmetry and its associated BRST charge. The main mathematical steps required to construct it are described. The algebra of constraints is, in general, a nonlinear Poisson algebra. In the nonlinear case the computation of the BRST charge by hand is hard. Itis explained how this computation can be made algorithmic. The main features of a recently created BRST computer algebra program are described. It can handle quadratic algebras very easily. Its capability to compute the BRST charge as a formal power series in the generic case of a cubic algebra is illustrated.
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H. Caprasse. BRST Charge and Poisson Algebras. Discrete Mathematics and Theoretical Computer Science, DMTCS, 1997, 1, pp.115-127. ⟨hal-00955694⟩

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