Details
| Original language | English |
|---|---|
| Journal | Fortschritte der Physik |
| Early online date | 3 Feb 2025 |
| Publication status | E-pub ahead of print - 3 Feb 2025 |
Abstract
In this paper, the development of a spectral triple-like construction on a configuration space of gauge connections is continued. It has previously been shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper, a central problem concerning the inclusion of fermions with half-integer spin into this framework is solved. The tangent space of the configuration space is mapped into a similar space based on spinors, and this map is used to construct a Dirac operator on the configuration space. A real structure acting in a Hilbert space over the configuration space is also constructed. Finally, it is shown that the self-dual and anti-self-dual sectors of the Hamiltonian of a nonperturbative quantum Yang-Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti-dual sectors are shown to emerge in a two-by-two matrix structure.
Keywords
- configuration space, noncommutative geometry, real structure, Yang–Mills theory
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Fortschritte der Physik, 03.02.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dirac Operators on Configuration Spaces
T2 - Fermions with Half-integer Spin, Real Structure, and Yang–Mills Quantum Field Theory
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
N1 - Publisher Copyright: © 2025 Wiley-VCH GmbH.
PY - 2025/2/3
Y1 - 2025/2/3
N2 - In this paper, the development of a spectral triple-like construction on a configuration space of gauge connections is continued. It has previously been shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper, a central problem concerning the inclusion of fermions with half-integer spin into this framework is solved. The tangent space of the configuration space is mapped into a similar space based on spinors, and this map is used to construct a Dirac operator on the configuration space. A real structure acting in a Hilbert space over the configuration space is also constructed. Finally, it is shown that the self-dual and anti-self-dual sectors of the Hamiltonian of a nonperturbative quantum Yang-Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti-dual sectors are shown to emerge in a two-by-two matrix structure.
AB - In this paper, the development of a spectral triple-like construction on a configuration space of gauge connections is continued. It has previously been shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper, a central problem concerning the inclusion of fermions with half-integer spin into this framework is solved. The tangent space of the configuration space is mapped into a similar space based on spinors, and this map is used to construct a Dirac operator on the configuration space. A real structure acting in a Hilbert space over the configuration space is also constructed. Finally, it is shown that the self-dual and anti-self-dual sectors of the Hamiltonian of a nonperturbative quantum Yang-Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti-dual sectors are shown to emerge in a two-by-two matrix structure.
KW - configuration space
KW - noncommutative geometry
KW - real structure
KW - Yang–Mills theory
UR - http://www.scopus.com/inward/record.url?scp=85216730636&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2410.07290
DO - 10.48550/arXiv.2410.07290
M3 - Article
AN - SCOPUS:85216730636
JO - Fortschritte der Physik
JF - Fortschritte der Physik
SN - 0015-8208
ER -