D. S. Kaparulin, S. L. Lyakhovich, A. A. Sharapov
We study the groups of local BRST cohomology associated to the systems of ordinary differential equations brought to the involutive normal form. Regarding these equations as governing the dynamics of a (non-)Lagrangian mechanical system, physical interpretation is provided for certain cohomology groups. These include the groups corresponding to global symmetries, conservation laws and Lagrange structures. It is shown that the space of Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization by means of Lagrange structures and the deformation quantization of weak Poisson brackets.
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http://arxiv.org/abs/1207.0594
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