A group method solving many-body systems in intermediate statistical representation Article Swipe
Yao Shen
,
Chi-Chun Zhou
,
Wu-Sheng Dai
,
Mi Xie
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1209/0295-5075/ac29f1
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1209/0295-5075/ac29f1
The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the unitary group. We prove a group theorem first, then using the theorem, we represent the Hamiltonian of the interacting many-body system by the Casimir operators of unitary group. The eigenvalues of Casimir operators could give the exact values of energy and thus solve those problems exactly. This method maps the interacting many-body system onto an intermediate statistical representation. We give the relation between the conjugacy-class operator of permutation group and the Casimir operator of unitary group in the intermediate statistical representation, called the Gentile representation. Bose and Fermi cases are two limitations of the Gentile representation. We also discuss the representation space of symmetric and unitary group in the Gentile representation and give an example of the Heisenberg model to demonstrate this method. It is shown that this method is effective to solve interacting many-body problems.
Related Topics
Concepts
Mathematics
Unitary group
Group (periodic table)
Unitary state
Heisenberg group
Operator (biology)
Hamiltonian (control theory)
Unitary representation
Pure mathematics
Group representation
Lie group
Quantum mechanics
Physics
Repressor
Law
Chemistry
Gene
Mathematical optimization
Biochemistry
Transcription factor
Political science
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1209/0295-5075/ac29f1
- OA Status
- green
- References
- 30
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3164517263
All OpenAlex metadata
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https://openalex.org/W3164517263Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1209/0295-5075/ac29f1Digital Object Identifier
- Title
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A group method solving many-body systems in intermediate statistical representationWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-09-01Full publication date if available
- Authors
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Yao Shen, Chi-Chun Zhou, Wu-Sheng Dai, Mi XieList of authors in order
- Landing page
-
https://doi.org/10.1209/0295-5075/ac29f1Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://export.arxiv.org/pdf/2105.12343Direct OA link when available
- Concepts
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Mathematics, Unitary group, Group (periodic table), Unitary state, Heisenberg group, Operator (biology), Hamiltonian (control theory), Unitary representation, Pure mathematics, Group representation, Lie group, Quantum mechanics, Physics, Repressor, Law, Chemistry, Gene, Mathematical optimization, Biochemistry, Transcription factor, Political scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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30Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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