Quantization of Midisuperspace Models

Villaseñor, Eduardo J. S.

doi:10.12942/lrr-2010-6

Cited by 25 publications

(28 citation statements)

References 214 publications

(385 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, these reduced models are usually of physical relevance in cosmology or in astrophysical situations. The so-called midisuperspace models [76,77], coming from reductions that keep an infinite number of degrees of freedom, are especially relevant from the technical point of view, since they capture at least some of the field complexity of general relativity. Among this kind of models, the simplest model with applications in cosmology is the family of Gowdy spacetimes [18] with linear polarization and with the spatial topology of a three-torus, T 3 .…”

Section: Uniqueness Of the Description For Quantum Gowdy Cos-molomentioning

confidence: 99%

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

View full text Add to dashboard Cite

In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaître-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations. * jacq@ciencias.unam.mx † mena@iem.cfmac.csic.es ‡ jvelhi@ubi.pt(2.1)By taking the direct sum of these two spaces, we get the complex vector space V + J ⊕ V − J , the elements of which can be written as (J turns out to be the same as V C , so that the complex vector spaces defined in Eq. (2.1) provide a splitting for the complexification of V . Besides, notice that every v in V can be decomposed asClearly, different complex structures will lead to distinct splittings for V C and, consequently, to different decompositions for v ∈ V . By extending the action of J from V to V C by complex linearity, we obtain that v + and v − are eigenvectors of J with eigenvalues i and −i,Given another complex structure, sayJ, its eigenvectors will satisfy relationships (2.2) with J replaced withJ. The eigenvectors ofJ and J are related byṽ. , x m , y 1 , . . . , y m )}. The standard (also called canonical) symplectic form is then. Equivalently, the standard symplectic form defines a skew-symmetric bilinear function on V [1], on C, and where we have used that Jv − = Jv + . A straightforward inspection shows that v, w J defines a Hermitian inner product on V + J ; that is,is a Hermitian inner product. This, together with the fact that any element of V + J is uniquely represented by an element of V (and vice versa), implies that the complex vector space V , with Hermitian inner product (2.7), and the complex vector space V + J , with Hermitian inner product (2.8), are (essentially) the same inner product spaces.B. The scalar field: Classical theory the unit function [see Eq. (2.11)]. Since observables on (S, Ω) can be obtained by taking linear combinations of products of natural observables Ω(φ, · ) and the unit function I (which provides the constant functions on S), the subspace 4 {I, Ω(φ, · ) | φ ∈ S} R of O qualifies as an admissible set of basic observables. This, together with the "naturalness and simplicity" of our choice, leads us to select the commented subspace as the set O 0 of fundamental (basic, or elementary) classical observables.By equipping the phase space (S, Ω) with a compatible complex structure J, the fi...

show abstract

Section: Uniqueness Of the Description For Quantum Gowdy Cos-molomentioning

confidence: 99%

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

View full text Add to dashboard Cite

show abstract

“…There is by now a vast literature on this proposal. This covers the homogeneous cosmological models, where this equation simplifies to a condition in quantum mechanics [2], to more complex systems with local dynamical degrees of freedom [3]. There remain however significant difficulties in both formulating the equation precisely, and in finding and interpreting meaningful solutions.…”

Section: Introductionmentioning

confidence: 99%

Does quantum gravity relate the constants of nature?

Husain

Singh

2019

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

The central equation of quantum gravity is the Wheeler-DeWitt equation. We give an argument suggesting that exact solutions of this equation give a surface in the space of coupling constants. This provides a mechanism for determining the cosmological constant as a function of the gravitational and other interaction constants. We demonstrate the idea by computing one such surface in a cosmological model. * Electronic address: vhusain@unb.ca † Electronic address: suprit.singh@unb.ca arXiv:1807.08704v2 [gr-qc] 31 Jul 2018

show abstract

“…Parametrized scalar fields have been recently used to explore the resolution of a number of technical issues related to the treatment of diffeomorphisms in loop quantum gravity [6,7] and in the search for boundary observables [8]. Moreover, some interesting gravitational models, such as Einstein-Rosen waves in vacuum or coupled to massless scalar fields, are known to be dynamically equivalent to a parametrized massless scalar field with cylindrical symmetry [9,10] (see also [11] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian description of the parametrized scalar field in bounded spatial regions

Margalef-Bentabol

Villaseñor

2016

Class. Quantum Grav.

View full text Add to dashboard Cite

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it.

show abstract

Quantization of Midisuperspace Models

Cited by 25 publications

References 214 publications

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Does quantum gravity relate the constants of nature?

Hamiltonian description of the parametrized scalar field in bounded spatial regions

Contact Info

Product

Resources

About