scholarly journals Nonperturbative one-loop effective action for QED with Yukawa couplings

2018 ◽  
Vol 33 (27) ◽  
pp. 1850157 ◽  
Author(s):  
Theodore N. Jacobson ◽  
Tonnis ter Veldhuis
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Background Field ◽  
Field Approximation ◽  
Chiral Anomaly ◽  
Dirac Fermion ◽  
Yukawa Couplings ◽  
Time Formalism ◽  
The One ◽  
The Relationship

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

scholarly journals Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 68 ◽  
Author(s):  
Ioseph Buchbinder ◽  
Evgeny Ivanov ◽  
Boris Merzlikin ◽  
Konstantin Stepanyantz
Keyword(s):  
Effective Action ◽  
Gauge Theories ◽  
Proper Time ◽  
Background Field ◽  
Field Method ◽  
Quantum Corrections ◽  
Supersymmetric Gauge Theories ◽  
Loop Approximation ◽  
Supersymmetric Gauge ◽  
The One

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

scholarly journals One-loop calculations in Lorentz-breaking theories and proper-time method

2021 ◽  
Author(s):  
Alysson Ferrari ◽  
Job Furtado Neto ◽  
Jose F. Assunção ◽  
Tiago Mariz ◽  
Albert Yu. Petrov
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Axial Vector ◽  
Constant Tensor ◽  
The One

Abstract We discuss applications of the proper-time method in various minimal Lorentz violating modifications of QED and present new results obtained with its use. Explicitly we calculate the complete one-loop Heisenberg-Euler effective action involving all orders in $F_{\mu\nu}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^{\mu}$ and the one involving the second-rank constant tensor $c^{\mu\nu}$.

CONVERGENCE OF DERIVATIVE AND INVERSE EFFECTIVE MASS EXPANSIONS FOR THE ONE LOOP EFFECTIVE ACTION

1987 ◽  
Vol 02 (05) ◽  
pp. 353-358 ◽  
Author(s):  
ROBERT J. PERRY ◽  
MING LI
Keyword(s):  
Effective Mass ◽  
Effective Action ◽  
Asymptotic Series ◽  
Background Field ◽  
Higher Order ◽  
Numerical Results ◽  
Derivative Expansion ◽  
Loop Correction ◽  
The One ◽  
Higher Order Corrections

Numerical results for the one loop correction to (ϕ4)2 are compared to results obtained from a derivative expansion and an expansion in inverse powers of the effective mass. We vary the scalar background field to illustrate when and why these expansions succeed, and how they break down. It is shown that both expansions behave like asymptotic series, with the approximation improving until higher order corrections grow in magnitude.

scholarly journals Background independent exact renormalisation

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Kevin Falls
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Beta Function ◽  
Background Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Gauge Invariant ◽  
Yang Mills ◽  
The One ◽  
Group Flow

AbstractA geometric formulation of Wilson’s exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov’s scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli–Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang–Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang–Mills beta function within a simple truncation of the Wilsonian effective action.

scholarly journals On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
I. L. Buchbinder ◽  
A. S. Budekhina ◽  
B. S. Merzlikin
Keyword(s):  
Effective Action ◽  
Sigma Model ◽  
Proper Time ◽  
Kähler Manifold ◽  
Quantum Structure ◽  
Harmonic Superspace ◽  
Component Structure ◽  
Covariant Derivatives ◽  
The One ◽  
Quantum Splitting

AbstractWe study the quantum structure of four-dimensional $${{\mathcal {N}}}=2$$ N = 2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $$\omega $$ ω . The model is described by harmonic superfield sigma-model metric $$g_{ab}(\omega )$$ g ab ( ω ) and two potential-like superfields $$L^{++}_{a}(\omega )$$ L a + + ( ω ) and $$L^{(+4)}(\omega )$$ L ( + 4 ) ( ω ) . In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly $${{\mathcal {N}}}=2$$ N = 2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary $$g_{ab}(\omega ), L^{++}_{a}(\omega ), L^{(+4)}(\omega )$$ g ab ( ω ) , L a + + ( ω ) , L ( + 4 ) ( ω ) , where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the $${{\mathcal {N}}}=2$$ N = 2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

Evolution of Coupling Constant in Hot QCD

1997 ◽  
Vol 06 (01) ◽  
pp. 45-64
Author(s):  
M. Chaichian ◽  
M. Hayashi
Keyword(s):  
Finite Temperature ◽  
Lorentz Invariance ◽  
Background Field ◽  
Field Method ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Time Formalism ◽  
Background Field Method ◽  
The One

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the breakdown of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.

scholarly journals On plasmon contribution to the hot A0 condensate

2019 ◽  
Vol 27 (2) ◽  
pp. 3-8
Author(s):  
O. A. Borisenko ◽  
V. V. Skalozub
Keyword(s):  
Effective Action ◽  
Field Component ◽  
Background Field ◽  
Internal Space ◽  
Long Distance ◽  
Standard Definition ◽  
Temporal Gauge ◽  
Condensation Phenomenon ◽  
The One ◽  
Correlation Corrections

In SU(2) gluodynamics, the Debye gluon contribution WD(A0) to the effective action of the temporal gauge field component (we consider A0 = const) in the background Rξext is calculated at high temperaturegauge. It is shown that at A0 ≠ 0 the standard definition k0 = 0 , |k| → 0 corresponds to long distance correlations for the longitudinal in internal space gluons. The transversal gluons become screened by the A0  background field. Therefore, they give zero contributions and have to be excluded from the correlation corrections. The total effective action accounting for the one-loop, two-loop, and correct WD(A0) satisfies Nielsen’s identity that proves gauge invariance of the A0 condensation phenomenon.

scholarly journals COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM

1998 ◽  
Vol 13 (20) ◽  
pp. 1623-1635 ◽  
Author(s):  
IOSEPH L. BUCHBINDER ◽  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Vector Multiplet ◽  
Harmonic Superspace ◽  
Background Field Method ◽  
Field Formalism ◽  
The One

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

Misreading Egypt

2018 ◽  
Author(s):  
Jesse Schotter
Keyword(s):  
New Media ◽  
Narrative Form ◽  
Experimental Film ◽  
Tower Of Babel ◽  
Avant Garde ◽  
Sergei Eisenstein ◽  
History Of ◽  
The One ◽  
The Relationship ◽  
Modern Technologies

The first chapter of Hieroglyphic Modernisms exposes the complex history of Western misconceptions of Egyptian writing from antiquity to the present. Hieroglyphs bridge the gap between modern technologies and the ancient past, looking forward to the rise of new media and backward to the dispersal of languages in the mythical moment of the Tower of Babel. The contradictory ways in which hieroglyphs were interpreted in the West come to shape the differing ways that modernist writers and filmmakers understood the relationship between writing, film, and other new media. On the one hand, poets like Ezra Pound and film theorists like Vachel Lindsay and Sergei Eisenstein use the visual languages of China and of Egypt as a more primal or direct alternative to written words. But Freud, Proust, and the later Eisenstein conversely emphasize the phonetic qualities of Egyptian writing, its similarity to alphabetical scripts. The chapter concludes by arguing that even avant-garde invocations of hieroglyphics depend on narrative form through an examination of Hollis Frampton’s experimental film Zorns Lemma.

Researching (with) Major Food Retailers

2015 ◽  
Vol 15 (3) ◽  
pp. 33-39 ◽  
Author(s):  
David Evans
Keyword(s):  
Food Systems ◽  
Academic Research ◽  
Social Scientists ◽  
Major Food ◽  
Food Retailers ◽  
Food Retailer ◽  
The One ◽  
The Uk ◽  
The Relationship ◽  
Opening Up

This paper considers the relationship between social science and the food industry, and it suggests that collaboration can be intellectually productive and morally rewarding. It explores the middle ground that exists between paid consultancy models of collaboration on the one hand and a principled stance of nonengagement on the other. Drawing on recent experiences of researching with a major food retailer in the UK, I discuss the ways in which collaborating with retailers can open up opportunities for accessing data that might not otherwise be available to social scientists. Additionally, I put forward the argument that researchers with an interest in the sustainability—ecological or otherwise—of food systems, especially those of a critical persuasion, ought to be empirically engaging with food businesses. I suggest that this is important in terms of generating better understandings of the objectionable arrangements that they seek to critique, and in terms of opening up conduits through which to affect positive changes. Cutting across these points is the claim that while resistance to commercial engagement might be misguided, it is nevertheless important to acknowledge the power-geometries of collaboration and to find ways of leveling and/or leveraging them. To conclude, I suggest that universities have an important institutional role to play in defining the terms of engagement as well as maintaining the boundaries between scholarship and consultancy—a line that can otherwise become quite fuzzy when the worlds of commerce and academic research collide.

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