Fermions at finite density in the path integral approach
Abstract We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the iε term that projects on the finite density ground state, and compute the path integral analyt...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2024)182 |
| _version_ | 1797276119988174848 |
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| author | Alessandro Podo Luca Santoni |
| author_facet | Alessandro Podo Luca Santoni |
| author_sort | Alessandro Podo |
| collection | DOAJ |
| description | Abstract We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the iε term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the U(1) symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler-Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas-van Alphen effect. Finally, we consider a (generalized) Gross-Neveu model for N interacting fermions at finite density. We compute its non-perturbative effective potential in the large-N limit, and discuss the fate of the U(1) vector and ℤ 2 A $$ {\mathbb{Z}}_2^A $$ axial symmetries. |
| first_indexed | 2024-03-07T15:23:45Z |
| format | Article |
| id | doaj.art-4ca67ea145b44c75ab1fd3163ba6f814 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-07T15:23:45Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4ca67ea145b44c75ab1fd3163ba6f8142024-03-05T17:27:30ZengSpringerOpenJournal of High Energy Physics1029-84792024-02-012024213310.1007/JHEP02(2024)182Fermions at finite density in the path integral approachAlessandro Podo0Luca Santoni1Department of Physics, Center for Theoretical Physics, Columbia UniversityUniversité Paris Cité, CNRS, Astroparticule et CosmologieAbstract We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the iε term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the U(1) symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler-Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas-van Alphen effect. Finally, we consider a (generalized) Gross-Neveu model for N interacting fermions at finite density. We compute its non-perturbative effective potential in the large-N limit, and discuss the fate of the U(1) vector and ℤ 2 A $$ {\mathbb{Z}}_2^A $$ axial symmetries.https://doi.org/10.1007/JHEP02(2024)182Finite Temperature or Finite DensityGlobal SymmetriesNonperturbative Effects |
| spellingShingle | Alessandro Podo Luca Santoni Fermions at finite density in the path integral approach Journal of High Energy Physics Finite Temperature or Finite Density Global Symmetries Nonperturbative Effects |
| title | Fermions at finite density in the path integral approach |
| title_full | Fermions at finite density in the path integral approach |
| title_fullStr | Fermions at finite density in the path integral approach |
| title_full_unstemmed | Fermions at finite density in the path integral approach |
| title_short | Fermions at finite density in the path integral approach |
| title_sort | fermions at finite density in the path integral approach |
| topic | Finite Temperature or Finite Density Global Symmetries Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP02(2024)182 |
| work_keys_str_mv | AT alessandropodo fermionsatfinitedensityinthepathintegralapproach AT lucasantoni fermionsatfinitedensityinthepathintegralapproach |