Moshe Shapiro 2008 J. Phys. A: Math. Theor. 41 175303 doi:10.1088/1751-8113/41/17/175303
Derivation of the relativistic 'proper-time' quantum evolution equations from canonical invariance
Moshe Shapiro
Show affiliationsBased on (1) the spectral resolution of the energy operator; (2) the linearity of correspondence between physical observables and quantum self-adjoint operators; (3) the definition of conjugate coordinate–momentum variables in classical mechanics; and (4) the fact that the physical point in phase space remains unchanged under (canonical) transformations between one pair of conjugate variables to another, we are able to show that 
, the proper-time rest-energy transformation matrices, are given as aexp(−iEsts/
), from which we obtain the proper-time rest-energy evolution equation 
. For special relativistic situations this equation can be reduced to the usual 
dynamical equations, where t is the 'reference time' and E is the total energy. Extension of these equations to accelerating frames is then provided.
- PACS
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03.65.Sq Semiclassical theories and applications
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 17 (2 May 2008)
Received 8 February 2008, in final form 10 March 2008
Published 15 April 2008
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Derivation of the relativistic 'proper-time' quantum evolution equations from canonical invariance
Moshe Shapiro 2008 J. Phys. A: Math. Theor. 41 175303
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