Group Quantization on Configuration Space
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Knowledge AreaMatemática Aplicada
SponsorsM. Navarro is grateful to the Spanish MEC for a postdoctoral FPU grant. M. Calixto thanks the Spanish MEC for a FPU grant.
PublisherAmerican Institute of Physics
Bibliographic CitationNAVARRO, Miguel, ALDAYA VALVERDE, Victor, CALIXTO MOLINA, Manuel. Group Quantization on Configuration Space. Journal of Mathematical Physics, 37 (206): 206-218, 1996. ISSN 0022-2488
KeywordsSimetria de grupo
Cuantización de grupos
New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the “quantizing group”) does not require, in general, the explicit construction of the phase space of the system, i.e., does not require the actual knowledgement of the general solution of the classical equations of motion: in many relevant cases an implicit construction of the group can be given, directly, on configuration space. As an application we construct the symmetry group for the conformally invariant massless scalar and electromagnetic fields and the scalar and Dirac fields evolving in a symmetric curved spacetime or interacting with symmetric classical electromagnetic fields. Further generalizations of the present procedure are also discussed and in particular the conditions under which non-abelian (mainly Kac-Moody) groups can be included.
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