On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not avai...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/10/2/60 |
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| author | Alejandro Corichi Juan D. Reyes Tatjana Vukašinac |
| author_facet | Alejandro Corichi Juan D. Reyes Tatjana Vukašinac |
| author_sort | Alejandro Corichi |
| collection | DOAJ |
| description | The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject. |
| first_indexed | 2024-03-07T22:10:46Z |
| format | Article |
| id | doaj.art-1946a491cdc243a18bddec6ad2cacc76 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-07T22:10:46Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-1946a491cdc243a18bddec6ad2cacc762024-02-23T15:36:44ZengMDPI AGUniverse2218-19972024-01-011026010.3390/universe10020060On Covariant and Canonical Hamiltonian Formalisms for Gauge TheoriesAlejandro Corichi0Juan D. Reyes1Tatjana Vukašinac2Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacán 58090, MexicoFacultad de Ingeniería, Universidad Autónoma de Chihuahua, Nuevo Campus Universitario, Chihuahua 31125, MexicoFacultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58000, MexicoThe Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject.https://www.mdpi.com/2218-1997/10/2/60hamiltonian formalismgauge theoriesfield theories with boundaries |
| spellingShingle | Alejandro Corichi Juan D. Reyes Tatjana Vukašinac On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories Universe hamiltonian formalism gauge theories field theories with boundaries |
| title | On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories |
| title_full | On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories |
| title_fullStr | On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories |
| title_full_unstemmed | On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories |
| title_short | On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories |
| title_sort | on covariant and canonical hamiltonian formalisms for gauge theories |
| topic | hamiltonian formalism gauge theories field theories with boundaries |
| url | https://www.mdpi.com/2218-1997/10/2/60 |
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