Quantum cosmology with Yang-Mills fields

Kapetanakis, D.; Koutsoumbas, G.; Lukas, André; Mayr, Peter

doi:10.1016/0550-3213(94)00441-g

Cited by 5 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[12] the correspondence between Lifshitz-harmonics [14] and the harmonics derived from the representation matrices of G [13] has been established up to spin J = 2. For the scalar harmonics and the purely transverse vector and tensor harmonics it has been found that…”

Section: Appendicesmentioning

confidence: 99%

“…According to ref. [12] this arises automatically if the field χ is assumed to be close to one of its "classical" values χ = ±1. This assumption is well justified for a small gauge coupling e in which case the wave function for χ is strongly peaked around these values [16] (see eq.…”

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

“…Here we will not reproduce this Lagrangian which has been determined in ref. [12] since in view of the wormhole wave function we are mainly interested in the Hamiltonian. To proceed in an explicit gauge invariant way we study the effect of an infinitesimal gauge transformation δA µ = ∇ µ U − [U, A µ ], U = u a T a on the perturbations :…”

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

“…[12]. Our conventions concerning the geometry of S 3 and the harmonics are summarized in appendix A.…”

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

“…A generalization which includes perturbations has been given in ref. [12]. In the next section we will briefly review some results of these papers which we will need.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Wormhole effects on Yang-Mills theory

Lukas¹

1995

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

In this paper wormhole effects on SO(3) YM theory are examined. The wormhole wave functions for the scalar, the vector and the tensor expansion modes are computed assuming a small gauge coupling which leads to an effective decoupling of gravity and YM theory. These results are used to determine the wormhole vertices and the corresponding effective operators for the lowest expansion mode of each type. For the lowest scalar mode we find a renormalization of the gauge coupling from the two point function and the operators tr(F 3 ), tr(F 2F ) from the three point function. The two point function for the lowest vector mode contributes to the gauge coupling renormalization only whereas the lowest tensor mode can also generate higher derivative terms.

show abstract

Section: Appendicesmentioning

confidence: 99%

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

“…[12]. Our conventions concerning the geometry of S 3 and the harmonics are summarized in appendix A.…”

Section: Harmonic Expansion Of So(3) Ym-theorymentioning

confidence: 99%

“…A generalization which includes perturbations has been given in ref. [12]. In the next section we will briefly review some results of these papers which we will need.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Wormhole effects on Yang-Mills theory

Lukas¹

1995

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

show abstract

Decoherence of Friedmann-Robertson-Walker geometries in the presence of massive vector fields with U(1) or SO(3) global symmetries

Bertolami

Moniz

1995

Nuclear Physics B

View full text Add to dashboard Cite

Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of midisuperspace models in the presence of scalar fields and the inhomogeneous modes corresponding either to gravitational or scalar fields. In this work, we propose an alternative model to study the decoherence of homogeneous and isotropic geometries where the scalar field is replaced by a massive vector field with a global internal symmetry. We study here the cases with U(1) and SO(3) global internal symmetries. The presence of a mass term breaks the conformal invariance and allows for the longitudinal modes of the spin-1 field to be present in the Wheeler-DeWitt equation. In the case of the U(1) global internal symmetry, we have only one single "classical" degree of freedom while in the case of the SO(3) global symmetry, we are led to consider a simple two-dimensional minisuperspace model. These minisuperspaces are shown to be equivalent to a set of coupled harmonic oscillators where the kinetic term of the longitudinal modes has a coefficient proportional to the inverse of the scale factor. The conditions for a suitable decoherence process and correlations between coordinate and momenta are established. The validity of the semi-classical Einstein equations when massive vector fields (Abelian and non-Abelian) are present is also discussed. correlation conditions (36)-(38) are indeed satisfied restricted to those environment modes. Notice then that J |B ′ J | 2 4B 2 rJ = J   1 4 Ω ′ J Ω J 2 + |β J | 2 4Ω 2 J

show abstract

Cosmological Einstein–Yang–Mills equations

Darian

Künzle

1997

Journal of Mathematical Physics

View full text Add to dashboard Cite

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU (n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU (n) and SO(n) where these homomorphisms correspond to unitary or orthogonal representations of the isotropy group. For some of the simpler cases the full system of the evolution equations are derived, for others we only determine the number of dynamical variables that remain after some mild fixing of the gauge.

show abstract

Quantum cosmology with Yang-Mills fields

Cited by 5 publications

References 30 publications

Wormhole effects on Yang-Mills theory

Wormhole effects on Yang-Mills theory

Decoherence of Friedmann-Robertson-Walker geometries in the presence of massive vector fields with U(1) or SO(3) global symmetries

Cosmological Einstein–Yang–Mills equations

Contact Info

Product

Resources

About