Path Integral Representation of Quantum Mechanics

2008 ◽  
pp. 1-54 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation

scholarly journals PATH INTEGRAL AND PSEUDOCLASSICAL ACTION FOR SPINNING PARTICLE IN EXTERNAL ELECTROMAGNETIC AND TORSION FIELDS

2000 ◽  
Vol 15 (24) ◽  
pp. 3861-3876 ◽  
Author(s):  
BODO GEYER ◽  
DMITRY GITMAN ◽  
ILYA L. SHAPIRO
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Integral Representation ◽  
Path Integral ◽  
Classical Limit ◽  
Equations Of Motion ◽  
Nonrelativistic Limit ◽  
Spinning Particle ◽  
Path Integral Representation ◽  
The Given

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a pseudoclassical action for a spinning particle. It is just a generalization of Berezin–Marinov action to the background under consideration. Pseudoclassical equations of motion in the nonrelativistic limit reproduce exactly the classical limit of the Pauli quantum mechanics in the same case. Quantization of the action appears to be nontrivial due to an ordering problem, which needs to be solved to construct operators of first-class constraints, and to select the physical sector. Finally the quantization reproduces the Dirac equation in the given background and, thus, justifies the interpretation of the action.

ANOTHER DERIVATION OF A SUPERPARTICLE ACTION

1991 ◽  
Vol 06 (21) ◽  
pp. 1977-1982 ◽  
Author(s):  
E. S. FRADKIN ◽  
SH. M. SHVARTSMAN
Keyword(s):  
Green Function ◽  
Integral Representation ◽  
Path Integral ◽  
Path Integral Representation ◽  
Chiral Superfield

It is shown that the reparametrization invariant superparticle action can be determined by constructing the path-integral representation for the causal Green function of a chiral superfield interacting with an external Maxwell superfield.

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