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Strongly Supercommuting Self-Adjoint Operators

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Abstract.

We introduce the notion of strong supercommutativity of self-adjoint operators on a \(\mathbb{Z}_2 \) -graded Hilbert space and give some basic properties. We clarify that strong supercommutativity is a unification of strong commutativity and strong anticommutativity. We also establish the theory of super quantization. Applications to supersymmetric quantum field theory and a fermion-boson interaction system are discussed.

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  1. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Tadahiro Miyao

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  1. Tadahiro Miyao
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Correspondence to Tadahiro Miyao.

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Miyao, T. Strongly Supercommuting Self-Adjoint Operators. Integr. equ. oper. theory 50, 505–535 (2004). https://doi.org/10.1007/s00020-003-1233-0

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  • DOI: https://doi.org/10.1007/s00020-003-1233-0

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