International Journal of Modern Physics. A
- ISSN 0217-751X
Roč. 24, 28-29 (2009), s. 5319-5340
Number of pages
20 s.
Language
eng - English
Country
SG - Singapore
Keywords
dissipative quantization ; non-Lagrangian system ; umbilical string
Subject RIV
BE - Theoretical Physics
R&D Projects
LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
CEZ
AV0Z10480505 - UJF-V (2005-2011)
UT WOS
000272093700007
Annotation
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.
