Higher gauge theory
In mathematical physics higher gauge theory is the general study of counterparts of gauge theory that involve higher-degree differential forms instead of the traditional connection forms of gauge theories.
Frameworks for higher gauge theory
[edit]There are several distinct frameworks within which higher gauge theories have been developed. Alvarez et al. [1] extend the notion of integrability to higher dimensions in the context of geometric field theories. Several works[2] of John Baez, Urs Schreiber and coauthors have developed higher gauge theories heavily based on category theory. Arthur Parzygnat [3] has a detailed development of this framework. An alternative approach,[4] motivated by the goal of constructing geometry over spaces of paths and higher-dimensional objects, has been developed by Saikat Chatterjee, Amitabha Lahiri, and Ambar N. Sengupta.
The mathematical framework for traditional gauge theory places the gauge potential as a 1-form on a principal bundle over spacetime. Higher gauge theories provide geometric and category-theoretic, especially higher category theoretic, frameworks for field theories that involve multiple higher differential forms.
See also
[edit]- Gauge theory
- Introduction to gauge theory
- Gauge group (mathematics)
- Yang–Mills theory
- Yang–Mills equations
References
[edit]- ^ Alvarez, Orlando; Ferreira, Luiz A.; Guillén, J. Sánchez (1998). "A new approach to integrable theories in any dimension". Nuclear Physics B. 529: 689–736.
- ^ Baez, John C.; Schreiber, Urs (2007). Categories in algebra, geometry and mathematical physics. Contemporary Mathematics. Vol. 431. Providence, RI: American Mathematical Society. pp. 7–30.
- ^ Parzygnat, Arthur (2015). "Gauge invariant surface holonomy and monopoles". Theory and Applications of Categories. 30: 1319–1428.
- ^ Chatterjee, Saikat; Lahiri, Ambitabha; Sengupta, Ambar N. (2017). "Connections on decorated path space bundles". Journal of Geometry and Physics. 112: 147–174.
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