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Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 46)

DOI: 10.1007/978-981-19-5678-2

ISBN: 978-981-19-5677-5

Publisher: Springer Nature Singapore - Springer Journals

Oct 19, 2022

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Chapter 1Abstract Supersymmetric Quantum Mechanics

Arai, Asao

Pages: 1 –11

[We review basic aspects of the mathematical theory of abstract supersymmetric quantum mechanics, which can be applied to supersymmetric quantum mechanics both with finite degrees of freedom and with infinite degrees of freedom, including supersymmetric quantum field theory.]
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Chapter 2Elements of the Theory of Fock Spaces

Arai, Asao

Pages: 13 –25

[We review the theory of Fock spaces within the scope of the following chapters (for more details, see [22]).]
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Chapter 3Q-space Representation of Boson Fock Space

Arai, Asao

Pages: 27 –33

[We review the so-called Q-space representation (a probability theoretical representation) of the boson Fock space over a Hilbert space. This representation is useful in analyzing quantum field models (e.g., [20, 34, 38, 61, 62]) and has important relations to infinite-dimensional stochastic...
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Chapter 4Boson–Fermion Fock Spaces and Abstract Supersymmetric Quantum Field Models

Arai, Asao

Pages: 35 –73

[We introduce some operators on the abstract boson–fermion Fock space, including exterior differential and Dirac operators, and describe fundamental properties of them. We present also abstract supersymmetric quantum field models.]
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Chapter 5Models in Supersymmetric Quantum Field Theory

Arai, Asao

Pages: 75 –98

[We construct in a mathematically rigorous way two-dimensional versions of the Wess–Zumino models in supersymmetric quantum field theory as an application of the theory of infinite-dimensional Dirac operators on the abstract boson–fermion Fock space presented in Chap. 4. Other supersymmetric...

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Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields

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