A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

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dc.creatorThienel, Hans-Peter
dc.date1995-11-22
dc.date.accessioned2026-07-07T10:58:39Z
dc.date.available2026-07-07T10:58:39Z
dc.descriptionIn the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic oscillator. Considering also $p$-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we end up with an analogous representation for the $D$-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. Emphasis is on calculus.
dc.description11 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/hep-th/9511155
dc.identifierhttp://arxiv.org/abs/hep-th/9511155
dc.identifierJ.Phys.A29:6983,1996
dc.identifierdoi:10.1088/0305-4470/29/21/028
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/187176
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleA Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry
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