Canonical analysis of field theories in the presence of boundaries: Maxwell <b>+</b> Pontryagin

Corichi, Alejandro; Vukašinac, Tatjana

doi:10.1088/1361-6382/ab778f

Cited by 3 publications

(17 citation statements)

References 41 publications

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“…Furthermore, this manuscript can be seen as a continuation of the work on gauge theories defined in regions with boundaries, following the ideas of [15,35]. There it was shown that when the action contains a boundary contribution with a time derivative, then a boundary contribution to the symplectic structure arises rather naturally.…”

Section: Introductionmentioning

confidence: 89%

“…It has three parts. In the first one, we briefly summarize the formalism of gauge theories in the presence of a boundary as developed in [15]. In the second one, we summarize the isolated horizon boundary conditions and its main geometrical constituents.…”

Section: Preliminariesmentioning

confidence: 99%

“…We shall start by recalling some of the main results of [15]. In that contribution the objective was to study gauge theories that could have a boundary term in the covariant (or canonical) action, containing time derivatives of the fields.…”

Section: Canonical Formalism For Gauge Theories Defined In Regions Wi...mentioning

confidence: 99%

“…The purpose of this manuscript is twofold. On the one hand, we are interested in exploring physical systems that can be analyzed from the perspective of a newly revised extension of the Dirac algorithm for theories defined with a region with a boundary [15]. Furthermore, as an application of the formalism, we are interested in making contact with research on isolated horizons and the corresponding Hamiltonian description on them.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Weakly isolated horizons: 3 + 1 decomposition and canonical formulations in self-dual variables

Corichi¹,

Reyes²,

Vukašinac³

2022

Class. Quantum Grav.

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The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. In particular, the deﬁnition of weakly isolated horizons (WIHs) as quasilocal generalizations of event horizons is purely geometrical, and is independent of the variables used in describing the gravitational ﬁeld. Here we consider a canonical decomposition of general relativity in terms of connection and vierbein variables starting from a ﬁrst order action. Within this approach, the information about the existence of a (weakly) isolated horizon is obtained through a set of boundary conditions on an internal boundary of the spacetime region under consideration. We employ, for the self-dual action, a generalization of the Dirac algorithm for regions with boundary. While the formalism for treating gauge theories with boundaries is unambiguous, the choice of dynamical variables on the boundary is not. We explore this freedom and consider diﬀerent canonical formulations for non-rotating black holes as deﬁned by WIHs. We show that both the notion of horizon degrees of freedom and energy associated to the horizon is not unique, even when the descriptions might be self-consistent. This represents a generalization of previous work on isolated horizons both in the exploration of this freedom and in the type of horizons considered. We comment on previous results found in the literature.

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Section: Introductionmentioning

confidence: 89%

Section: Preliminariesmentioning

confidence: 99%

Section: Canonical Formalism For Gauge Theories Defined In Regions Wi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Weakly isolated horizons: 3 + 1 decomposition and canonical formulations in self-dual variables

Corichi¹,

Reyes²,

Vukašinac³

2022

Class. Quantum Grav.

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“…with α = (κ |γ|)/2. Since we can not find all the "velocities" with these expressions 17 , we can define the following primary constraints,…”

Section: B1 Hamiltonian Analysismentioning

confidence: 99%

Constructing the theory at the boundary, its dynamics and degrees of freedom

Rubalcava-Garcia

2020

Preprint

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Given a theory in a region of space-time with boundaries, defined by a Lagrangian, we propose a method to find the corresponding theory at the boundary (either space-like or time-like), that allows us to identify the degrees of freedom at the boundary without any gauge fixing nor further assumptions a priori. We start by finding the corresponding action principle at the boundary. From this, we can find the corresponding equations of motion, the symmetries and degrees of freedom at the boundary. Then we characterise the degrees of freedom at the boundary. We exemplify this method by analysing the broadly studied 3-dimensional Abelian Chern-Simons theory. We found, through the Hamiltonian framework, that the boundary theory has one degree of freedom that can be characterised by the chiral boson: the Quantum Hall edge modes. We also find a correspondence between a gauge fixing in the bulk with a boundary condition and discuss whether this is enough to have a well-posed action principle and the possible scenarios.

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On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories

Corichi,

Reyes,

Vukašinac

2024

Universe

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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.

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Canonical analysis of field theories in the presence of boundaries: Maxwell + Pontryagin

Cited by 3 publications

References 41 publications

Weakly isolated horizons: 3 + 1 decomposition and canonical formulations in self-dual variables

Weakly isolated horizons: 3 + 1 decomposition and canonical formulations in self-dual variables

Constructing the theory at the boundary, its dynamics and degrees of freedom

On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories

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