Visualising quantum effective action calculations in zero dimensions

Millington, Peter; Saffin, Paul M.

doi:10.1088/1751-8121/ab37e6

Cited by 21 publications

(26 citation statements)

References 38 publications

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“…Zerodimensional field theory was also used to study densityfunctional theory [55,56,58] and applied to fermionic fields [53]. Recently, it was used to study and visualize 2PI effective actions [59] -also in the FRG framework [60,62,63].…”

Section: A the Partition Function In Zero Dimensionsmentioning

confidence: 99%

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Koenigstein,

Steil,

Wink

et al. 2021

Preprint

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The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows to reliably treat the emergence of non-analytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. We work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higherdimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

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Section: A the Partition Function In Zero Dimensionsmentioning

confidence: 99%

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Koenigstein,

Steil,

Wink

et al. 2021

Preprint

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show abstract

“…This is shown explicitly in the case of a zero-dimensional field theory with spontaneous symmetry breaking in Ref. [30] (see Fig. 3(a) therein).…”

mentioning

confidence: 73%

“…The placement of the functional arguments reflects the fact that both the number and nature of the saddle points depend on the configuration (φ, ∆), see Ref. [30].…”

mentioning

confidence: 99%

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Alternative flow equation for the functional renormalization group

et al. 2019

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We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point source of the 2PI effective action to be associated consistently with the regulator of the renormalization group flow. We show that this procedure leads to a flow equation that differs from that obtained in the standard approach based on the average one-particle irreducible effective action.

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“…In case the vacuum structure is generated by radiative corrections in the first place, one can deal with it using the two-particle irreducible effective action and evaluate the partition function by expanding about the self-consistent solution to the quantum-corrected one and two-point functions, as explained in Refs. [15,23,25].…”

Section: Callan-coleman Formalism and The Bouncementioning

confidence: 99%

Gradient effects on false vacuum decay in gauge theory

Cruz

Garbrecht

et al. 2020

Phys. Rev. D

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We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as nonderivative one-loop corrections.

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Visualising quantum effective action calculations in zero dimensions

Cited by 21 publications

References 38 publications

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Alternative flow equation for the functional renormalization group

Gradient effects on false vacuum decay in gauge theory

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