Towards an algorithmisation of the Dirac constraint formalism

Details Towards an algorithmisation of the Dirac constraint formalism Towards an algorithmisation of the Dirac constraint formalism

2006-11-09

arxiv.org/abs/math-ph/0611021v1

Global Integrability of Field Theories / Proceedings of GIFT 2006. J.Calmet, W.M.Seiler, R.W.Tucker (Eds.), Cocroft Institute,

Physics

Mathematical Physics

15 pages, Proceedings of GIFT 2006, Cocroft Institute, Daresbury (UK), November 1-3, 2006

Scientific paper

Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian systems, we describe an algorithmic scheme of computation of the complete set of constraints, their separation into subsets of first and second class constraints as well as the construction of a generator of local symmetry transformations. The proposed scheme is exemplified by considering the so-called light-cone Yang-Mills mechanics with an SU(2) gauge structure group.

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