Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.04555 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917732381884416 |
|---|---|
| author | Abram, Valentino Brunetti, Romeo |
| author_facet | Abram, Valentino Brunetti, Romeo |
| contents | In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions made by several collegues. The treatment is restricted to contractible spacetimes of globally hyperbolic nature in dimensions $d\ge 4$. In particular, we construct the classical Møller maps intertwining the configuration spaces of charged and uncharged fermions. In the last part, as a first step towards a quantization of the theory, we explore the combination of the classical Møller maps with Hadamard bidistributions and prove that they are involutive isomorphisms (algebraically and topologically) between suitable (formal) algebras of functionals (observables) over the configuration spaces of charged and uncharged Dirac fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Møller maps for Dirac fields in external backgrounds Abram, Valentino Brunetti, Romeo Mathematical Physics In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions made by several collegues. The treatment is restricted to contractible spacetimes of globally hyperbolic nature in dimensions $d\ge 4$. In particular, we construct the classical Møller maps intertwining the configuration spaces of charged and uncharged fermions. In the last part, as a first step towards a quantization of the theory, we explore the combination of the classical Møller maps with Hadamard bidistributions and prove that they are involutive isomorphisms (algebraically and topologically) between suitable (formal) algebras of functionals (observables) over the configuration spaces of charged and uncharged Dirac fields. |
| title | Møller maps for Dirac fields in external backgrounds |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2401.04555 |