Particle creation, renormalizability conditions and the mass-energy spectrum in gravity theories of quadratic Lagrangians

Kleidis, K.; Papadopoulos, D.

doi:10.1088/0264-9381/15/8/007

Cited by 2 publications

(1 citation statement)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, both superstring theories (Candelas et al 1985, Green et al 1987 and the one-loop approximation of quantum gravity (Kleidis and Papadopoulos 1998), suggest that the presence of quadratic terms in the gravitational action is a priori expected. Therefore, in connection to the semi-classical interaction previously stated, the question that arises now is, what the functional form of the corresponding renormalizable energy-momentum tensor might be, if the simplest quadratic curvature term, R 2 , is included in the description of the classical gravitational field.…”

Section: Quadratic Interactionmentioning

confidence: 99%

Interactive quadratic gravity

Kleidis¹,

Kuiroukidis²,

Papadopoulos³

2002

Physics Letters B

View full text Add to dashboard Cite

A quadratic semiclassical theory, regarding the interaction of gravity with a massive scalar quantum field, is considered in view of the renormalizable energymomentum tensor in a multi-dimensional curved spacetime. According to it, a self-consistent coupling between the square curvature term R 2 and the quantum field Φ(t, x) should be introduced in order to yield the "correct" renormalizable energy-momentum tensor in quadratic gravity theories. The subsequent interaction discards any higher-order derivative terms from the gravitational field equations, but, in the expence, it introduces a geometric source term in the wave equation for the quantum field. Unlike the conformal coupling case (∼ RΦ 2 ), this term does not represent an additional "mass" and, therefore, the quantum field interacts with gravity not only through its mass (or energy) content (∼ Φ 2 ), but, also, in a more generic way (R 2 Φ). Within this context, we propose a general method to obtain mode-solutions for the quantum field, by means of the associated Green's function in an anisotropic six-dimensional background.

show abstract

Section: Quadratic Interactionmentioning

confidence: 99%

Interactive quadratic gravity

Kleidis¹,

Kuiroukidis²,

Papadopoulos³

2002

Physics Letters B

View full text Add to dashboard Cite

show abstract

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

Particle creation, renormalizability conditions and the mass-energy spectrum in gravity theories of quadratic Lagrangians

Cited by 2 publications

References 71 publications

Interactive quadratic gravity

Interactive quadratic gravity

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

Contact Info

Product

Resources

About