Orthosymplectically invariant functions in superspace

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3462685· OSTI ID:21476542

Coulembier, K; De Bie, H; Sommen, F ^[1]

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1. Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally, the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.

• OSTI ID: 21476542
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3462685; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FUNCTIONS
HARMONIC OSCILLATORS
INVARIANCE PRINCIPLES
SCHROEDINGER EQUATION
SPACE
SYMMETRY
SYMMETRY GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS