Y Ohnuki 2004 J. Phys. A: Math. Gen. 37 1373 doi:10.1088/0305-4470/37/4/021
Path integral representations for a system constrained on a manifold
Y Ohnuki
Show affiliationsA systematic study is made of path integral representations for a particle constrained to move on a manifold diffeomorphic to SD by applying the irreducible representations of the Dirac algebra on it. Especially, we derive two types of path integral representation for this system, one of which is of a new form with a simple and compact expression, and the other is a rigorous version of the Faddeev–Senjanovic formula. It is also shown that the parameter α 
[0, 1) specifying the irreducible representation for D = 1 has a close connection with the Aharonov–Bohm gauge potential produced by the magnetic flux 
.
- PACS
- MSC
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58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (See also 22E65, 57S05)
81S40 Path integrals (See also 58D30)
70H45 Constrained dynamics, Dirac's theory of constraints (See also 70F20, 70F25, 70Gxx)
- Subjects
- Dates
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Issue 4 (30 January 2004)
Received 9 July 2003, in final form 6 October 2003
Published 9 January 2004
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Path integral representations for a system constrained on a manifold
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