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QUANTIZATION OF NON-LAGRANGIAN SYSTEMS

DENIS KOCHAN

Department of Theoretical Physics, Nucl. Phys. Inst. AS, Řež, Czech Republic

Department of Theoretical Physics, FMFI UK, Bratislava, Slovak Republic

https://doi.org/10.1142/S0217751X0904748XCited by:1 (Source: Crossref)

Abstract

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.

Dedicated to my daughter Zoe on the occasion of her birth.

Keywords:

PACS: 01.70.+w, 02.40.Yy, 03.65.Ca, 45.20.-d

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