Quantum effective action for degenerate vector field theories

Ruf, Michael; Steinwachs, Christian F.

doi:10.1103/physrevd.98.085014

Cited by 10 publications

(7 citation statements)

References 51 publications

(95 reference statements)

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“…Nevertheless, for higher derivative theories, the high number of derivatives in the vertices in general lead to a high number of loop momenta in the numerators of Feynman integrals. Moreover, additional loop momenta arise in the numerator due to the propagator expansion (8). Ultimately, this might lead to very high-rank tensors Q µ1...µ2ω which render this brute-force implementation inefficient.…”

Section: One-loop Integralsmentioning

confidence: 99%

“…Second, different propagators (of equal or different spin) might differ in their masses m i . Performing the propagator expansion (8) for each of these propagators, the denominator of the integrand of the resulting Feynman integrals acquires the schematic structure…”

Section: Extension To Integrals With Multiple Different Propagatorsmentioning

confidence: 99%

“…In particular, the generalized Schwinger-DeWitt algorithm reduces the closed-form calculation of one-loop divergences in field theories with higher derivatives and non-minimal fluctuation operators to the evaluation of products of nested commutators and a few 'universal functional traces' [5]. There are, however, important cases in which these algorithms are either not directly applicable, such as for fluctuation operators with a degenerate principle part [6,7,8], or become practically inefficient, such as in higher derivative theories like e.g. in Galileon models relevant in cosmology [9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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Combinatorial aspects in the one-loop renormalization of higher derivative theories

Steinwachs

2019

Preprint

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An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this way, a generic one-loop diagram is reduced to a sum of vacuum diagrams. The logarithmically divergent part can be extracted by power counting arguments. In case of higher derivative theories, the standard implementation of this procedure on a computer algebra system can become quickly inefficient due to a high proliferation of terms coming from the intermediate replacement of high-rank tensor-integrals with symmetrized product of metric tensors. In this note we present a simple combinatorial solution to this problem which makes the implementation much more efficient. This method is especially relevant in the renormalization of higher derivative theories, but might as well be integrated as a standard routine in existing computer algebra programs designed to automatize Feynman diagrammatic calculations.

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Section: One-loop Integralsmentioning

confidence: 99%

Section: Extension To Integrals With Multiple Different Propagatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combinatorial aspects in the one-loop renormalization of higher derivative theories

Steinwachs

2019

Preprint

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“…Generalized vector field models in cosmology have been investigated in [1][2][3][4][5][6][7][8][9][10][11]. The renormalization structure of the generalized Proca theory in curved spacetime has been discussed in [12][13][14][15][16][17][18]. The simplest models with an additional propagating degree of freedom, are scalar-tensor theories and geometric modifications such as f (R) gravity, see e.g.…”

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confidence: 99%

Geometrized quantum Galileons

Heisenberg

Steinwachs

2020

J. Cosmol. Astropart. Phys.

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We investigate the renormalization structure of the scalar Galileon model in flat spacetime by calculating the one-loop divergences in a closed geometric form. The geometric formulation is based on the definition of an effective Galileon metric and allows to apply known heat-kernel techniques. The result for the one-loop divergences is compactly expressed in terms of curvature invariants of the effective Galileon metric and corresponds to a resummation of the divergent one-loop contributions of all n-point functions. The divergent part of the one-loop effective action therefore serves as generating functional for arbitrary n-point counterterms. We discuss our result within the Galileon effective field theory and give a brief outlook on extensions to more general Galileon models in curved spacetime.Keywords: modified gravity, quantum field theory in curved spacetime, effective field theory, physcis of the early universe arXiv:1909.07111v1 [hep-th]

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“…The perturbative algorithm underlying the generalized SDW technique relies on the non-degeneracy of the principal symbol D of the operator F. There are, however, important physical theories for which the principal symbol of the fluctuation operator is degenerate so that the (generalized) SDW algorithm is not directly applicable. In such cases, more general methods are required; see [76][77][78] for heat-kernel calculations involving operators with degenerate principal part and [79,80] for operators with Laplacians constructed from an effective (background field-dependent) metric. In the context of Lifshitz theories, the development of heat-kernel techniques for anisotropic operators has recently been initiated [81][82][83].…”

Section: F(∇)mentioning

confidence: 99%

Towards a Unitary, Renormalizable, and Ultraviolet-Complete Quantum Theory of Gravity

Steinwachs

2020

Front. Phys.

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For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry that derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Hořava gravity, a quantum Lifshitz field theory of gravity characterized by an anisotropic scaling between space and time, unitarity and renormalizability can be retained while Lorentz invariance is sacrificed at high energies and must emerge only as approximate symmetry at low energies. This article reviews various approaches to perturbative quantum gravity, with a particular focus on recent progress in the quantization of Hořava gravity, supporting its theoretical status as a unitary, renormalizable, and ultraviolet-complete quantum theory of gravity.

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Quantum effective action for degenerate vector field theories

Cited by 10 publications

References 51 publications

Combinatorial aspects in the one-loop renormalization of higher derivative theories

Combinatorial aspects in the one-loop renormalization of higher derivative theories

Geometrized quantum Galileons

Towards a Unitary, Renormalizable, and Ultraviolet-Complete Quantum Theory of Gravity

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