Dirac’s algorithm in the presence of boundaries: a practical guide to a geometric approach

Díaz, Bogar; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.

doi:10.1088/1361-6382/ab436b

Cited by 23 publications

(34 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the most efficient way to get the previous formulation is to use the GNH method, it can also be obtained by employing the geometric implementation of Dirac's algorithm [14,15].…”

Section: Symplectic Formulation For the Holst Actionmentioning

confidence: 99%

Concise symplectic formulation for tetrad gravity

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although the most efficient way to get the previous formulation is to use the GNH method, it can also be obtained by employing the geometric implementation of Dirac's algorithm [14,15].…”

Section: Symplectic Formulation For the Holst Actionmentioning

confidence: 99%

Concise symplectic formulation for tetrad gravity

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Then, from (4. 19) we obtain that components of the Hamiltonian vector field in the bulk are £ t φ := (X H ) φ = u , (4.21)…”

Section: Hamiltonian Analysis: Maxwell + Chern-simonsmentioning

confidence: 99%

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

Corichi¹,

Vukašinac²

2020

Class. Quantum Grav.

View full text Add to dashboard Cite

We study the canonical Hamiltonian analysis of gauge theories in the presence of boundaries. While the implementation of Dirac's program in the presence of boundaries, as put forward by Regge and Teitelboim, is not new, there are some instances in which this formalism is incomplete. Here we propose an extension to the Dirac formalism -together with the Regge-Teitelboim strategy,-that includes generic cases of field theories. We see that there are two possible scenarios, one where there is no contribution from the boundary to the symplectic structure and the other case in which there is one, depending on the dynamical details of the starting action principle. As a concrete system that exemplifies both cases, we consider a theory that can be seen both as defined on a four dimensional spacetime region with boundaries -the bulk theory-, or as a theory defined both on the bulk and the boundary of the region -the mixed theory-. The bulk theory is given by the 4-dimensional Maxwell + U (1) Pontryagin action while the mixed one is defined by the 4-dimensional Maxwell + 3-dimensional U (1) Chern-Simons action on the boundary. Finally, we show how these two descriptions of the same system are connected through a canonical transformation that provides a third description. The focus here is in defining a consistent formulation of all three descriptions, for which we rely on the geometric formulation of constrained systems, together with the extension of the Dirac-Regge-Teitelboim (DRT) formalism put forward in the manuscript.

show abstract

“…For instance, it gives information about the compatibility of the dynamical equations in the interior of M and in the boundary ∂M . The Dirac algorithm can, in fact, be thought of as a way to obtain conditions (constraints) that must be imposed on the configuration variables and their conjugate momenta to have consistent dynamics (here we will follow [14], similar information can be obtained by using the GNH method [15][16][17]). The constraints restrict the possible initial data for the field equations.…”

Section: Hamiltonian Formulation For the Generalized Modelsmentioning

confidence: 99%

“…The implementation of the geometric form of the Dirac algorithm described in [14] is now a straightforward exercise. The main step is solving for the Hamiltonian vector field X in the equation…”

Section: Jhep10(2019)121mentioning

confidence: 99%

“…The Hamiltonian description for the actions discussed in the paper has been obtained by relying on the geometric approach developed in [14] to specifically deal with field theories defined in regions with boundaries. Although Hamiltonian methods are often used as a first step to quantization, we have taken advantage of them in a purely classical context to get several interesting results.…”

Section: Jhep10(2019)121mentioning

confidence: 99%

See 1 more Smart Citation

Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary

Díaz

Margalef-Bentabol

Villaseñor

2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchař actions on manifolds with boundary. In some cases, they describe wellknown models-either at the boundary or in the bulk-such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kuchař model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.

show abstract

Dirac’s algorithm in the presence of boundaries: a practical guide to a geometric approach

Cited by 23 publications

References 23 publications

Concise symplectic formulation for tetrad gravity

Concise symplectic formulation for tetrad gravity

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

Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary

Contact Info

Product

Resources

About