QUANTUM CANONICAL TRANSFORMATIONS AS INTEGRAL TRANSFORMATIONS

Hietarinta, Jarmo

doi:10.1103/PhysRevD.25.2103

QUANTUM CANONICAL TRANSFORMATIONS AS INTEGRAL TRANSFORMATIONS

Jarmo Hietarinta
(
- Turku U.
)

Jun, 1981

32 pages

Published in:

Phys.Rev.D 25 (1982) 2103

DOI:

10.1103/PhysRevD.25.2103

Report number:

TURKU-FTL-R18

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Abstract: (APS)

We discuss how the Hamiltonian changes in quantum canonical transformations. To the operator H^(p^,q^) one can associate (in a given ordering rule) a c-number function H(p,q). It is this function that appears in the action of the phase-space path integral. A quantum canonical transformation H^→H^′ can now be expressed as an integral transformation H′(p¯,q¯)=∫dpdqT(p¯,q¯;p,q)H(p,q). The kernel T is constructed explicitly for point transformations and for the p=−q¯, q=p¯ reflection by studying changes of variables in the path integral. The ordering dependence of T is displayed. The invariance of commutation rules is also discussed.

QUANTUM MECHANICS: PATH INTEGRAL
KINEMATICS: PHASE SPACE
QUANTUM MECHANICS: COMMUTATION RELATIONS
FUNCTIONAL ANALYSIS
APPROXIMATION: semiclassical
MATHEMATICAL METHODS

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Figures(0)

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