Kinematic quantum states for the Teleparallel Equivalent of General Relativity

Okołów, Andrzej

doi:10.1007/s10714-013-1653-3

Cited by 21 publications

(36 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, the constructions described in [1] and [5] are particular examples of the construction presented in [4]. Thus the result to be achieved here means that the families {D λ , π λλ ′ } λ∈Λ obtained in these three papers can be seen as originating from families of factorized Hilbert spaces.…”

Section: Discussionmentioning

confidence: 86%

“…In the original paper [1] this idea was applied to linear phase spaces. Further development of the projective construction presented in [3,4,5,6,7] consisted in applying this idea to more and more general phase spaces including finally the one underlying Loop Quantum Gravity (LQG).…”

Section: Projective Construction Of Quantum States and Its Possible Flawmentioning

confidence: 99%

“…2. the application [5] to the Teleparallel Equivalent of General Relativity and a related toy-model [12].…”

Section: Partial Solutionsmentioning

confidence: 99%

“…The notion of family of factorized Hilbert spaces was introduced in [6] and the application of the projective construction to LQG with the SU (2) symmetry presented in [7] is based on this notion. However, as we will show in Appendix A, spaces of projective quantum states constructed in the earlier papers [1,4,5] can also be seen as derived from families of factorized Hilbert spaces.…”

Section: For Every λmentioning

confidence: 99%

See 3 more Smart Citations

A modification of the projective construction of quantum states for field theories

Kijowski

Okołów

2017

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

The projective construction of quantum states for field theories may be flawedin some cases the construction may possibly lead to spaces of quantum states which are "too small" to be used in quantization of field theories. Here we present a slight modification of the construction which is free from this flaw. * This is an author-created copyedited version of an article accepted for publication in Journal of Mathematical Physics. The definitive publisher authenticated version is available online at http://dx.

show abstract

Section: Discussionmentioning

confidence: 86%

Section: Projective Construction Of Quantum States and Its Possible Flawmentioning

confidence: 99%

“…2. the application [5] to the Teleparallel Equivalent of General Relativity and a related toy-model [12].…”

Section: Partial Solutionsmentioning

confidence: 99%

Section: For Every λmentioning

confidence: 99%

See 2 more Smart Citations

A modification of the projective construction of quantum states for field theories

Kijowski

Okołów

2017

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The need to include surfaces in the labels was already recognized by Okołów in [24,25]. The label set he was using is however not immediately applicable to the non-Abelian case, which requires, as we will see, to impose more restrictive conditions on the relative disposition of the edges and surfaces.…”

Section: Label Setmentioning

confidence: 99%

Projective loop quantum gravity. I. State space

Lanéry

Thiemann

2016

Journal of Mathematical Physics

View full text Add to dashboard Cite

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [14] to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [24] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels.If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.

show abstract

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

Okołów

2013

Gen Relativ Gravit

Self Cite

View full text Add to dashboard Cite

We present a new Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like 3 + 1 decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.

show abstract

Kinematic quantum states for the Teleparallel Equivalent of General Relativity

Cited by 21 publications

References 29 publications

A modification of the projective construction of quantum states for field theories

A modification of the projective construction of quantum states for field theories

Projective loop quantum gravity. I. State space

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

Contact Info

Product

Resources

About