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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.06674 |
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| _version_ | 1866916586205478912 |
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| author | Töpfel, Sebastian Geißel, Andreas Braun, Jens |
| author_facet | Töpfel, Sebastian Geißel, Andreas Braun, Jens |
| contents | We discuss subtleties in the calculation of loop integrals in studies of hot and dense systems as they appear in both perturbative and non-perturbative approaches. To be specific, we address subtleties which appear in situations where the order of integration, differentiation, and limit processes plays a crucial role. For example, this applies to computations of the effective action and the computation of momentum-dependent correlation functions. In particular, the zero-temperature limit is delicate in systems with fermions because of the presence of discontinuities at the Fermi surface. We provide a general discussion of scenarios where the computation and evaluation of loop integrals in the context of relativistic theories requires particular attention as a change of the order of the involved mathematical operations may lead to a different result. Our general considerations are then illustrated with the aid of concrete examples, namely by the computation of masses from fully momentum-dependent correlation functions in the context of the Gross-Neveu-Yukawa model and quantum electrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subtleties in the calculation of correlation functions for hot and dense systems Töpfel, Sebastian Geißel, Andreas Braun, Jens Nuclear Theory High Energy Physics - Theory We discuss subtleties in the calculation of loop integrals in studies of hot and dense systems as they appear in both perturbative and non-perturbative approaches. To be specific, we address subtleties which appear in situations where the order of integration, differentiation, and limit processes plays a crucial role. For example, this applies to computations of the effective action and the computation of momentum-dependent correlation functions. In particular, the zero-temperature limit is delicate in systems with fermions because of the presence of discontinuities at the Fermi surface. We provide a general discussion of scenarios where the computation and evaluation of loop integrals in the context of relativistic theories requires particular attention as a change of the order of the involved mathematical operations may lead to a different result. Our general considerations are then illustrated with the aid of concrete examples, namely by the computation of masses from fully momentum-dependent correlation functions in the context of the Gross-Neveu-Yukawa model and quantum electrodynamics. |
| title | Subtleties in the calculation of correlation functions for hot and dense systems |
| topic | Nuclear Theory High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.06674 |