Canonical Lifts in Multisymplectic De Donder-Weyl Hamiltonian Field Theories
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917733682118656 |
|---|---|
| author | Guerra IV, Arnoldo Román-Roy, Narciso |
| author_facet | Guerra IV, Arnoldo Román-Roy, Narciso |
| contents | In this paper, we define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder-Weyl Hamiltonian first-order field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether's theorem. The Klein-Gordon field, the Polyakov bosonic string, and Einstein-Cartan gravity in 3 + 1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07847 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical Lifts in Multisymplectic De Donder-Weyl Hamiltonian Field Theories Guerra IV, Arnoldo Román-Roy, Narciso Mathematical Physics High Energy Physics - Theory Differential Geometry {\it Primary}: 53D42, 70S05, 83C05, {\it Secondary}: 35Q75, 35Q76, 53Z05, 70H50, 83C99 In this paper, we define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder-Weyl Hamiltonian first-order field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether's theorem. The Klein-Gordon field, the Polyakov bosonic string, and Einstein-Cartan gravity in 3 + 1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint. |
| title | Canonical Lifts in Multisymplectic De Donder-Weyl Hamiltonian Field Theories |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry {\it Primary}: 53D42, 70S05, 83C05, {\it Secondary}: 35Q75, 35Q76, 53Z05, 70H50, 83C99 |
| url | https://arxiv.org/abs/2402.07847 |