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Abstract: The effective approach to quantum dynamics allows a reformulation of theDirac quantization procedure for constrained systems in terms of aninfinite-dimensional constrained system of classical type. For semiclassicalapproximations, the quantum constrained system can be truncated to finite sizeand solved by the reduced phase space or gauge-fixing methods. In particular,the classical feasibility of local internal times is directly generalized toquantum systems, overcoming the main difficulties associated with the generalproblem of time in the semiclassical realm. The key features of local internaltimes and the procedure of patching global solutions using overlappingintervals of local internal times are described and illustrated by two quantummechanical examples. Relational evolution in a given choice of internal time ismost conveniently described and interpreted in a corresponding choice of gaugeat the effective level and changing the internal clock is, therefore,essentially achieved by a gauge transformation. This article complements theconceptual discussion in arXiv:1009.5953.



Author: Martin Bojowald, Philipp A Hoehn, Artur Tsobanjan

Source: https://arxiv.org/







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