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Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators
by Guner Muarem
Submission summary
| Authors (as registered SciPost users): | Guner Muarem |
| Submission information | |
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| Preprint Link: | scipost_202212_00038v2 (pdf) |
| Date accepted: | Aug. 11, 2023 |
| Date submitted: | Jan. 5, 2023, 12:27 p.m. |
| Submitted by: | Guner Muarem |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper we use the canonical complex structure $\boldsymbol{\mathbb{J}}$ on $\boldsymbol{\mathbb{R}^{2n}}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold. Moreover, we prove that the algebra of these Dirac operators is isomorphic to the Lie algebra $\boldsymbol{\mathfrak{su}(1,2)}$ which leads to the Howe dual pair $(\boldsymbol{\operatorname{U}(n)},\boldsymbol{\mathfrak{su}(1,2))}$.
Author comments upon resubmission
List of changes
1) "As a matter of fact" is used too often, and can usually be removed (for example, remove it in the Abstract) => Adapted 2) Abstract: analogon -> analogue. => fixed 3) First line of Introduction: put the meaning of CAR just behind it (as you did for CCR) => fixed 4) Section 3.3: you use already ∂zj and ∂¯¯¯zj, but define it only in the next subsession. => moved above 5) Last paragraph of 3.4: ... with H an holomorphic function in several variables (i.e. is -> in) => fixed 6) Section 4, after the table: 2. We have three copies of ... (i.e. two -> three). => fixed 7) Sentence -3 of Section 4: Recall that these are ... (i.e. this -> these). => fixed 8) List in Section 5: replace m by n => fixed
Published as SciPost Phys. Proc. 14, 038 (2023)