Towards perturbative renormalization of 
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 quantum field theory

Felski, Alexander; Bender, Carl M.; Klevansky, S. P.; Sarkar, Sarben

doi:10.1103/physrevd.104.085011

Cited by 14 publications

(7 citation statements)

References 49 publications

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“…4π 2 γ − 1 + log a 2 = 0 (58) 9 One loop involving two Yukawa vertices contributes to the fermion self-energy (see fig. 1(a)).…”

Section: Dynamical Mass Generationmentioning

confidence: 99%

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PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

Mavromatos,

Sarkar,

Soto

2021

Preprint

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We consider the renormalisation properties of non-Hermitian Yukawa theories involving a pseudoscalar (axion) field. More generally these models provide simple paradigms for the study of the quantum behaviour of non-Hermitian (but PT -symmetric) fermionic models as higher dimensional field theories. The flow between of PT -symmetric and Hermitian fixed points under the renormalisation group flows is examined.

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“…4π 2 γ − 1 + log a 2 = 0 (58) 9 One loop involving two Yukawa vertices contributes to the fermion self-energy (see fig. 1(a)).…”

Section: Dynamical Mass Generationmentioning

confidence: 99%

“…For purely bosonic theories the path integral has been used to derive a novel nonperturbative expansion for timeordered Green functions [8][9][10]. In [10] it has been emphasised that renormalisation may lead to features of nonHermiticity to arise, even when the starting point lies within a Hermitian framework.…”

mentioning

confidence: 99%

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

Mavromatos,

Sarkar,

Soto

2021

Preprint

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“…This paper presents new classes of solutions for the case in which the Euclidean spacetime dimension D is noninteger and the power of the scalar interaction may differ from four. Generalizing the power of the interaction is natural in the context of the δ-expansion [16][17][18] approach to quantum field theory and in the field of P T -symmetric quantum field theory [19][20][21][22][23][24][25][26]. Thus, instead of action (2), we consider the more general action…”

Section: Introductionmentioning

confidence: 99%

New Classes of Solutions for Euclidean Scalar Field Theories

Bender,

Sarkar

2024

Universe

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This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in D-dimensional spacetime. These solutions are found by exploiting the dimensional consistency of the radial differential equation for a single massless scalar field, which allows it to transform into an autonomous equation. For massive theories, the radial equation is not exactly solvable, but the massless solutions provide useful approximations to the results for the massive case. The solutions presented here depend on the power of the interaction and on the spatial dimension, both of which may be noninteger. Scalar equations arising in the study of conformal invariance fit into this framework, and classes of new solutions are found. These solutions exhibit two distinct behaviors as D→2 from above.

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“…Examples include: non-Hermitian deformations of the Dirac Lagrangian with a parity-odd, anti-Hermitian mass term [13][14][15][16][17] (see also Ref. [18]), theories of massive second-order fermions [19,20], scalar [16,17,[21][22][23] and fermionic [14,22,24] field theories with non-Hermitian mass mixing matrices, non-Hermitian Yukawa theories [14,[25][26][27][28], scalar theories with complex [29][30][31][32][33][34][35][36] or wrong-sign [37][38][39] self-interactions, theories exhibiting spontaneous symmetry breaking [40][41][42][43][44][45][46] and topological defects [47][48][49][50][51], holographic settings [52,53], and non-Hermitian Dirac materials in the context of condensed matter physics…”

Section: Introductionmentioning

confidence: 99%

IR/UV mixing from local similarity maps of scalar non-Hermitian field theories

Chernodub

Millington

2022

Phys. Rev. D

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Pseudo-Hermitian field theories possess a global continuous "similarity" symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavour scalar or fermion mixing, and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterised by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties.

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Towards perturbative renormalization of ϕ2(iϕ)ϵ quantum field theory

Cited by 14 publications

References 49 publications

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

New Classes of Solutions for Euclidean Scalar Field Theories

IR/UV mixing from local similarity maps of scalar non-Hermitian field theories

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