Isospectral local Hermitian theory for the $\mathcal{PT}$-symmetric $iϕ^3$ quantum field theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909428303790080 |
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| author | Li, Yi-Da Wang, Qing |
| author_facet | Li, Yi-Da Wang, Qing |
| contents | We propose a new method to calculate perturbatively the isospectral Hermitian theory for the $\mathcal{PT}$-symmetric $iϕ^3$ quantum field theory in $d$ dimensions, whose result is local. The result of the new method in $1$ dimension reproduces our previous result in the $ix^3$ quantum mechanics, and the new method can be seen as a generalization of our previous method to quantum field theory. We also find the isospectral local Hermitian theory has the same form in all dimensions and differs in coefficients only, and our previous results in quantum mechanics can be used directly to determine the form of the isospectral local Hermitian quantum field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isospectral local Hermitian theory for the $\mathcal{PT}$-symmetric $iϕ^3$ quantum field theory Li, Yi-Da Wang, Qing High Energy Physics - Theory High Energy Physics - Phenomenology We propose a new method to calculate perturbatively the isospectral Hermitian theory for the $\mathcal{PT}$-symmetric $iϕ^3$ quantum field theory in $d$ dimensions, whose result is local. The result of the new method in $1$ dimension reproduces our previous result in the $ix^3$ quantum mechanics, and the new method can be seen as a generalization of our previous method to quantum field theory. We also find the isospectral local Hermitian theory has the same form in all dimensions and differs in coefficients only, and our previous results in quantum mechanics can be used directly to determine the form of the isospectral local Hermitian quantum field theory. |
| title | Isospectral local Hermitian theory for the $\mathcal{PT}$-symmetric $iϕ^3$ quantum field theory |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2412.10732 |