On renormalisation of λϕ<sup>4</sup>field theory in curved space-time. I

Bunch, T S; Panangaden, Prakash; Parker, Leonard

doi:10.1088/0305-4470/13/3/022

Cited by 74 publications

(57 citation statements)

References 10 publications

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“…3,2002 The State Space of Perturbative QFT in Curved Spacetimes 655 of R n . 3,2002 The State Space of Perturbative QFT in Curved Spacetimes 655 of R n .…”

Section: Iv2 Proof Of Lemma Iii2mentioning

confidence: 99%

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

Hollands¹,

Ruan²

2002

Ann. Henri Poincaré

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The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains the Wick-polynomials of the free field as well as their time-ordered products, and hence, by the well-known rules of perturbative quantum field theory, also the observables (up to finite order) of interest for the interacting quantum field theory. We then determine the space of continuous states on this algebra. Our result is that this space consists precisely of those states whose truncated n-point functions of the free field are smooth for all n = 2, and whose two-point function has the singularity structure of a Hadamard fundamental form. A crucial role in our analysis is played by the positivity property of states. On the technical side, our proof involves functional analytic methods, in particular the methods of microlocal analysis.

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“…3,2002 The State Space of Perturbative QFT in Curved Spacetimes 655 of R n . 3,2002 The State Space of Perturbative QFT in Curved Spacetimes 655 of R n .…”

Section: Iv2 Proof Of Lemma Iii2mentioning

confidence: 99%

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

Hollands¹,

Ruan²

2002

Ann. Henri Poincaré

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“…This is explicitely displayed by (10.29) if the &functions are substituted in favour of the covariant ones defined in (2.5). In the special case of true scalar fields (w = 0) it reduces to results obtained earlier on the basis of functional integral [27], [75] or canonical [28]- [30] quantization. Next, with (10.12) one can derive the free propagator.…”

Section: Survey On the Measuresmentioning

confidence: 54%

“…Investigations concerned renormalizability, gravitationally induced symmetry breaking, particle production, backreaction on the gravitational field, interaction effects and others studied by canonical as well as functional integral techniques. (For a list of more classical papers see [13] - [30] and references therein). With the understanding of these theories during the last years it became also possible to investigate the behaviour of nonabelian gauge theories in curved spacetime mainly by exploiting functional integral techniques too [31]- [49].…”

Section: Introductionmentioning

confidence: 99%

Functional Methods for Arbitrary Densities in Curved Spacetime

Basler¹

1993

Fortschr. Phys.

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This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived.

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“…Further, a subset of the four-loop diagrams were summed in order to generate the counterterms dependent on the curvature of spacetime. All the nonlocal, state-dependent divergences associated with the renormalization program in curved space [3] were explicitly considered and to the order worked were shown to cancel.…”

Section: Introductionmentioning

confidence: 99%

Subleading divergences for scalar field theory in three dimensions

Huish

1995

Phys. Rev. D

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We complete a previous investigation into the renormalization of interacting scalar field theory in three dimensions using the background-field method. The divergent four-loop vacuum diagrams associated with flat space and contributing to the effective action are summed. All nonpolynomial terms associated with subdivergent diagrams are canceled by counterterm insertions in graphs of lower order. The remaining divergences are local polynomials in the renormalized couplings and we give the counterterms associated with these terms. We also list the renormalization group functions through four loops. Combined with previous results we can conclude that the theory remains renormalizable in a spacetime of arbitrary curvature up to four-loop order.

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On renormalisation of λϕ⁴field theory in curved space-time. I

Cited by 74 publications

References 10 publications

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

Functional Methods for Arbitrary Densities in Curved Spacetime

Subleading divergences for scalar field theory in three dimensions

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On renormalisation of λϕ4field theory in curved space-time. I

Cited by 74 publications

References 10 publications

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

Functional Methods for Arbitrary Densities in Curved Spacetime

Subleading divergences for scalar field theory in three dimensions

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On renormalisation of λϕ⁴field theory in curved space-time. I