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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 2, Pages 287–301
DOI: https://doi.org/10.4213/tmf6045 (Mi tmf6045) 		 
Fundamental solutions of the equations of quantum mechanics as distributions and distinctive properties of the Dirac equation solutions

A. A. Beilinson

Peoples Friendship University of Russia
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DOI: https://doi.org/10.4213/tmf6045
Abstract: We show that the causal Green's functions for interacting particles in external fields in both relativistic quantum mechanics (for the Dirac electron) and nonrelativistic quantum mechanics can be obtained as distributions if the free-particle Green's functions are used and equations for the corresponding test functions are chosen. We study quantum properties of solutions of the Dirac equations.
Keywords: causal Green's function, Wiener measure, Euclidean Dirac measure, denumerable additivity of measures, absolute additivity of measures, induced measure.
Received: 13.06.2006
Revised: 21.08.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 2, Pages 681–692
DOI: https://doi.org/10.1007/s11232-007-0053-9
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Language: Russian
Citation: A. A. Beilinson, “Fundamental solutions of the equations of quantum mechanics as distributions and distinctive properties of the Dirac equation solutions”, TMF, 151:2 (2007), 287–301; Theoret. and Math. Phys., 151:2 (2007), 681–692
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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