Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

Radenkovic, Tijana; Vojinović, Marko

doi:10.3390/sym12040620

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…Of course, due to antisymmetry, the nonzero µ blocks take negative values of the corresponding blocks, in accordance with (34), (35), and (36). The three independent nonzero blocks are chosen as…”

Section: Diffeomorphismsmentioning

confidence: 64%

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Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

et al. 2023

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When discussing the gauge symmetries of any theory, the Henneaux–Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux–Teitelboim transformations and the resulting gauge group in the general case and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

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Section: Diffeomorphismsmentioning

confidence: 64%

“…After discussing the Chern-Simons theory as a toy example, we move to the more important case of the 3BF theory. This theory is relevant for building models of quantum gravity; see [8,20,21,33,35]. Therefore, it is important to study its gauge symmetry and, in particular, the role of HT transformations.…”

Section: Ht Symmetry In 3bf Theorymentioning

confidence: 99%

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

et al. 2023

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“…In addition to the construction of a full quantum theory of gravity, there are also many additional possible studies of the classical constrained 3BF action. For example, a full Hamiltonian analysis of the 3BF action has been done for the example of scalar electrodynamics [26], and then also for a general choice of a Lie 3-group [27], and the complete gauge symmetry group has been discussed in detail [27,28]. Also, it is worth looking into the idea of imposing the simplicity constraints using a spontaneous symmetry breaking mechanism, and some work has already begun in this area.…”

Section: Discussionmentioning

confidence: 99%

Higher category theory and n-groups as gauge symmetries for quantum gravity

Nikolić,

Obrić,

Radenković

et al. 2023

J. Phys.: Conf. Ser.

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Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n-group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a topological action called nBF action, living on a corresponding n-principal bundle over a spacetime manifold. Similarly as for the Plebanski action, one can deform the topological nBF action by adding appropriate simplicity constraints, in order to describe the correct dynamics of both gravity and matter fields. Specifically, one can describe the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter. In addition, the properties of the gauge n-group structure open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, in a similar way to the ordinary gauge group that prescribes the spectrum of gauge vector bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

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“…All the above actions are topological, in the sense that they do not contain any local propagating degrees of freedom [44,45]. In this sense, they are not very interesting for the description of realistic physics, which should feature nontrivial dynamics.…”

Section: Topological Nbf Theoriesmentioning

confidence: 99%

Topological invariant of 4-manifolds based on a 3-group

Radenkovic

Vojinović

2022

J. High Energ. Phys.

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We study a generalization of 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF action for a general 3-group and a 4-dimensional spacetime manifold $$ \mathcal{M} $$ M 4. This state sum coincides with Porter’s TQFT for d = 4 and n = 3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum Z remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2BF action with the underlying 2-group structure.

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Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

Cited by 7 publications

References 16 publications

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

Higher category theory and n-groups as gauge symmetries for quantum gravity

Topological invariant of 4-manifolds based on a 3-group

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