Marsden{endash}Weinstein reduction on graded symplectic manifolds

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531902· OSTI ID:467261

Baguis, P; Stavracou, T ^[1]

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1. Centre de Physique Theorique, CNRS, Luminy, Case 907-F-13288, Marseille, Cedex 9 (France)

We extend the Marsden{endash}Weinstein reduction of Hamiltonian systems with symmetry to the category of graded manifolds. We define free, proper, and symplectic actions in the graded setting; especially for the symplectic actions of graded Lie groups, it is possible to speak about momentum mappings. We also examine the reduction of the graded Hamiltonian derivations which determines the dynamics on the reduced phase space for constrained supersystems with symmetry. We apply the general formalism to specific examples, thus constructing graded (complex) projective spaces, and proving that the coadjoint orbits of graded Lie groups are reduced graded symplectic manifolds. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 467261
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
GEOMETRY
HAMILTONIANS
LIE GROUPS
MATHEMATICAL MANIFOLDS
PHASE SPACE
SUPERSYMMETRY