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Towards an algorithmisation of the Dirac constraint formalism. (English) Zbl 1256.70009

Calmet, J. (ed.) et al., Global integrability of field theories. Proceedings of GIFT 2006, Cockcroft Institute, Daresbury, UK, November 1–3, 2006. Karlsruhe: Universitätsverlag Karlsruhe (ISBN 3-86644-035-9/pbk). 135-154 (2006).
Summary: Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Gröbner 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 \(\text{SU}(2)\) gauge structure group.
For the entire collection see [Zbl 1170.37001].

MSC:

70H45 Constrained dynamics, Dirac’s theory of constraints
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
81T13 Yang-Mills and other gauge theories in quantum field theory

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