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BRST charge and Poisson algebras. (English) Zbl 0940.81039

Author’s summary: 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. It is explained how this computation can be made algorithmic. The main features of a recently created BRST computer algebra program (REDUCE) are described. (This has been developed jointly with A. Burnel and A. Dresse, Int. J. Mod. Phys. C 5, No. 6, 1035-1047 (1994) reviewed in Zbl 0940.81039 above). 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.

MSC:

81T70 Quantization in field theory; cohomological methods
81-08 Computational methods for problems pertaining to quantum theory
17B63 Poisson algebras
81T13 Yang-Mills and other gauge theories in quantum field theory
17-08 Computational methods for problems pertaining to nonassociative rings and algebras

Citations:

Zbl 0940.81039
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