Correlation functions of scalar field theories from homotopy algebras
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909481036677120 |
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| author | Okawa, Yuji |
| author_facet | Okawa, Yuji |
| contents | We present expressions for correlation functions of scalar field theories in perturbation theory using quantum $A_\infty$ algebras. Our expressions are highly explicit and can be used for theories both in Euclidean space and in Minkowski space including quantum mechanics. Correlation functions at a given order of perturbation theory can be calculated algebraically without using canonical quantization or the path integral, and we demonstrate it explicitly for $φ^3$ theory. We show that the Schwinger-Dyson equations are satisfied as an immediate consequence of the form of the expressions based on quantum $A_\infty$ algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_05366 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Correlation functions of scalar field theories from homotopy algebras Okawa, Yuji High Energy Physics - Theory We present expressions for correlation functions of scalar field theories in perturbation theory using quantum $A_\infty$ algebras. Our expressions are highly explicit and can be used for theories both in Euclidean space and in Minkowski space including quantum mechanics. Correlation functions at a given order of perturbation theory can be calculated algebraically without using canonical quantization or the path integral, and we demonstrate it explicitly for $φ^3$ theory. We show that the Schwinger-Dyson equations are satisfied as an immediate consequence of the form of the expressions based on quantum $A_\infty$ algebras. |
| title | Correlation functions of scalar field theories from homotopy algebras |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2203.05366 |