Quantum field theory in curved spacetime

Birrell, N. D.; Davies, Paul

doi:10.1017/cbo9780511622632.005

Cited by 100 publications

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“…But this is not the case, as we will see, so Z[ρ] and its derivatives are not well defined 6 . As we have already said in the case of quantum filed theory in curved space time we only deal with two point functions.…”

Section: Introductionmentioning

confidence: 93%

“…[6] eqs. (3.131, 2, 3) and corresponds to an expansion in the metric g µν (x) and its derivatives, precisely to orders 0, 2, 4,...in these derivatives.…”

Section: The Expert Reader May Go Directly To Section V and Consider mentioning

confidence: 99%

“…We just quote the number of the equation of reference [6] at the beginning of each of them. In sections III, IV, and V we will use reference [5] for the same purpose in the λφ 4 case.…”

Section: The Expert Reader May Go Directly To Section V and Consider mentioning

confidence: 99%

“…But, if we add three "H" terms to the gravitational lagrangian which are linear combinations of the three terms of eq. (23): i. e., linear combinations of R 2 , R µν R µν , R αβγδ R αβγδ , and ✷R, (there are only three "H" terms because there is a relation among the last four terms) and renormalize the three corresponding coefficients (known as α, β, γ) the theory becomes renormalizable and finite (see [6] eqs. (6.52) to (6.56)).…”

Section: A Renormalization Using Dimensional Regularizationmentioning

confidence: 99%

“…Phrased in another way: in this paper we will find the short distance singularity in two quantum field theory models and we will show that if these singularities are substracted the theory turns out to be finite. The substraction of short distance singularities has being essentially used for many years, e. g., in Quantum Field Theory in Curved Space-Time, [4], [6], [7] (and other chapters of quantum field theory e. g. [5] chapter 5), but it was not considered as a general method with a rational motivation, as we are now trying to prove.…”

Section: Introductionmentioning

confidence: 99%

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Castagnino

2001

International Journal of Theoretical Physics

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The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of distributions (and worse defined mathematical objects). Some of them are eliminated defining a multiplication based in dimensional regularization while others disappear considering the states as functionals over the observables space. Non renormalizable theories turn to be finite, but anyhow they are endowed with infinite arbitrary constants.

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Section: Introductionmentioning

confidence: 93%

“…[6] eqs. (3.131, 2, 3) and corresponds to an expansion in the metric g µν (x) and its derivatives, precisely to orders 0, 2, 4,...in these derivatives.…”

Section: The Expert Reader May Go Directly To Section V and Consider mentioning

confidence: 99%

“…We just quote the number of the equation of reference [6] at the beginning of each of them. In sections III, IV, and V we will use reference [5] for the same purpose in the λφ 4 case.…”

Section: The Expert Reader May Go Directly To Section V and Consider mentioning

confidence: 99%

Section: A Renormalization Using Dimensional Regularizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Castagnino

2001

International Journal of Theoretical Physics

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The conformal status of ο = -3/2 Brans-Dicke cosmology

Dąbrowski¹,

Denkiewicz

Blaschke

2007

Ann. Phys.

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Following recent fit of supernovae data to Brans-Dicke theory which favours the model with ω = −3/2 [1] we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit ω = −3/2 is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with ω = −3/2 gives a border between a standard scalar field model and a ghost/phantom model.In this paper we show that in ω = −3/2 Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for k = −1 case. Further we show that this k = −1 case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in ω = −3/2 Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.

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Conformal transformations and conformal invariance in gravitation

Dąbrowski¹,

Garecki²,

Blaschke³

2009

Ann. Phys.

104

115

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Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy-momentum tensor. We show the subtlety of the matter energy-momentum conservation law which refers to the fact that the conformal transformation "creates" an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is "created" due to work done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R 2 , R ab R ab , R abcd R abcd and the Gauss-Bonnet invariant in a spacetime of an arbitrary dimension. Finally, we present the conformal transformation rules in the fashion of the duality transformations of the superstring theory.In such a case the transitions between conformal frames reduce to a simple change of the sign of a redefined conformal factor.

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Quantum field theory in curved spacetime

Cited by 100 publications

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The conformal status of ο = -3/2 Brans-Dicke cosmology

Conformal transformations and conformal invariance in gravitation

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