QUANTIZATION OF NON-LAGRANGIAN SYSTEMS

0338822 - ÚJF 2010 RIV SG eng J - Journal Article
Kochan, Denis
QUANTIZATION OF NON-LAGRANGIAN SYSTEMS.
International Journal of Modern Physics. A. Roč. 24, 28-29 (2009), s. 5319-5340. ISSN 0217-751X. E-ISSN 1793-656X
R&D Projects: GA MŠMT(CZ) LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : dissipative quantization * non-Lagrangian system * umbilical string
Subject RIV: BE - Theoretical Physics
Impact factor: 0.941, year: 2009

A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.
Permanent Link: http://hdl.handle.net/11104/0182493