Topology of the Misner space and its $$g$$ g -boundary

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

doi:10.1007/s10714-014-1755-6

Cited by 5 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We illustrate now how the GNH idea can be used to implement the Dirac algorithm with a simple mechanical example: a plane pendulum described as a constrained system. 12 Let us consider the configuration space Q = R 3 (so that TQ = R 3 × R 3 R 6 ) and take the Lagrangian…”

Section: An Example: the Pendulummentioning

confidence: 99%

See 1 more Smart Citation

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

Díaz

Margalef-Bentabol

Villaseñor

2019

Class. Quantum Grav.

View full text Add to dashboard Cite

The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay, Nester, and Hinds (GNH) to deal with singular Hamiltonian systems. We pay special attention to the specific issues raised by the presence of boundaries and provide a number of significant examples-among them field theories related to general relativity-to illustrate the main features of our approach.

show abstract

Section: An Example: the Pendulummentioning

confidence: 99%

“…When dealing with bounded systems, it is often interesting to find out to what extent it is possible to locate physical degrees of freedom either at the bulk or at the boundaries [11,12]. In this regard, it is appropriate to mention condensed matter physics (topological insulators and related systems).…”

Section: Introductionmentioning

confidence: 99%

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

Díaz

Margalef-Bentabol

Villaseñor

2019

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…This topology does not present the commented drawback and can be developed further. Of course, this modification of the topology will not solve magically all the problems of these boundaries, but it suggests possible improvements and opens the opportunity to re-study them (see, for instance, [23]).…”

Section: Completions Of Spacetimes T 2 -Separability and C-boundary mentioning

confidence: 99%

Hausdorff separability of the boundaries for spacetimes and sequential spaces

Flores

Herrera

Sánchez

2016

Journal of Mathematical Physics

View full text Add to dashboard Cite

There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator L. As emphasized in a classical article by Geroch, Liang and Wald, some of them have the property, commonly regarded as a drawback, that there are points of the spacetime M non T 1 -separated from points of the boundary ∂M .Here we show that this problem can be solved from a general topological viewpoint. In particular, there is a canonical minimum refinement of the topology in the completion M which T 2 -separates the spacetime M and its boundary ∂M -no matter the type of completion one chooses. Moreover, we analyze the case of sequential spaces and show how the refined T 2 -separating topology can be constructed from a modification L * of the original limit operator L. Finally, we particularize this procedure to the case of the causal boundary and show how the separability of M and ∂M can be introduced as an abstract axiom in its definition.

show abstract

“…However, this breaks down when there are second-class constraints, for then one is forced to introduce Dirac brackets, rendering this advantage null in that case. An equivalent approach of a geometric nature is provided by the Gotay-Nester-Hinds (GNH) algorithm [3][4][5][6][7][8][9]. The central idea is to search for a "stable submanifold" supporting a Hamiltonian vector field whose integral curves, suitably projected, provide the solutions to the equations of motion.…”

Section: Introductionmentioning

confidence: 99%

Dirac Geometric Approach for the Unimodular Holst Action

Díaz,

Villaseñor,

Salas

2024

Mathematics

View full text Add to dashboard Cite

We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional elements, such as parametrization, complex fields, or considering the Barbero–Immirzi parameter as imaginary. We show that, by using a geometric implementation of the Dirac algorithm, a comprehensive analysis of the theory can be conducted without relying on these additional ingredients. The resulting theory reproduces the behavior of metric unimodular gravity.

show abstract

Topology of the Misner space and its $$g$$ g -boundary

Cited by 5 publications

References 11 publications

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

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

Hausdorff separability of the boundaries for spacetimes and sequential spaces

Dirac Geometric Approach for the Unimodular Holst Action

Contact Info

Product

Resources

About