A study of gauge-invariant non-local interactions

1954 ◽  
Vol 223 (1155) ◽  
pp. 468-481 ◽  
Keyword(s):  
Quantum Theory ◽  
Gauge Invariance ◽  
Local Interactions ◽  
Gauge Invariant ◽  
Invariance Properties ◽  
Finite Theory ◽  
Non Local ◽  
The One ◽  
Dimensional Integral

The paper investigates the possibility of introducing ‘non-local’ interactions, i. e. interactions represented by four-dimensional integral operations, in order to eliminate divergences in the quantum theory of interacting fields. In particular, a type of equation is discussed which preserves all the required invariance properties, including gauge invariance and macroscopic causality. It turns out that equations of this type still give divergent results. The origin of these divergences is discussed, and it is shown that if there is any way of formulating a finite theory it would have to be very different from the one investigated here.

scholarly journals DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

2007 ◽  
Vol 22 (21) ◽  
pp. 3605-3620 ◽  
Author(s):  
E. M. C. ABREU ◽  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Gauge Invariance ◽  
Zero Mode ◽  
Mass Term ◽  
Gauge Invariant ◽  
Embedding Method ◽  
Symplectic Embedding ◽  
The One ◽  
Topological Term

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

scholarly journals C-projection and monopole condensation in QCD

2014 ◽  
Vol 29 ◽  
pp. 1460210
Author(s):  
Y. M. Cho
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Integral Expression ◽  
Gauge Invariant ◽  
Invariant Integral ◽  
Infra Red ◽  
The Stability ◽  
The One

We show that the monopole condensation is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence, and show that the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation.

scholarly journals ONE-PARTICLE AND COLLECTIVE ELECTRON SPECTRA IN HOT AND DENSE QED AND THEIR GAUGE DEPENDENCE

1998 ◽  
Vol 13 (21) ◽  
pp. 1719-1728 ◽  
Author(s):  
O. K. KALASHNIKOV
Keyword(s):  
Gauge Invariance ◽  
Electron Spectrum ◽  
Particle Spectrum ◽  
Gauge Invariant ◽  
Long Wavelength ◽  
Gauge Dependence ◽  
Electron Spectra ◽  
Zero Momentum ◽  
Collective Spectrum ◽  
The One

The one-particle electron spectrum is found for hot and dense QED and its properties are investigated in comparison with the collective spectrum. It is shown that the one-particle spectrum (in any case its zero momentum limit) is gauge-invariant, but the collective spectrum, being qualitatively different, is always gauge-dependent. The exception is the case m,μ=0 for which the collective spectrum long wavelength limit demonstrates the gauge invariance as well.

scholarly journals On the one-loop calculations with Reggeized quarks

2017 ◽  
Vol 32 (40) ◽  
pp. 1750207 ◽  
Author(s):  
Maxim Nefedov ◽  
Vladimir Saleev
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Action ◽  
Gauge Invariance ◽  
Effective Field ◽  
Loop Correction ◽  
Gauge Invariant ◽  
The One ◽  
Regge Limit

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and [Formula: see text]-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop [Formula: see text] amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

The free field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Gauge Invariance ◽  
Maxwell Equations ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Initial Conditions ◽  
Free Field ◽  
Maxwell Theory ◽  
Gauge Invariant ◽  
Massive Vector ◽  
The One

This chapter studies the structure of Maxwell’s equations in a vacuum and the action from which they are derived, while emphasizing the consequences of their gauge invariance. Gauge invariance, on the one hand, allows one of the components of the magnetic potential to be chosen freely. Here, the chapter shows how the gauge-invariant version of the Maxwell equations in the vacuum can also be derived directly by extremizing. On the other hand, the chapter argues that gauge invariance imposes a constraint on the initial conditions such that in the end the general solution has only two ‘degrees of freedom’. Finally, the chapter develops the Hamiltonian formalisms in the Maxwell theory and compares them to the formalisms using non-gauge-invariant or massive vector fields.

Surfing the Quantum World

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Musical Instrument ◽  
Popular Science ◽  
Quantum Spin ◽  
Exclusion Principle ◽  
Maximum Height ◽  
Core Concepts ◽  
The Many ◽  
The One

Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Etienne Blanco ◽  
Andreas van Hameren ◽  
Piotr Kotko ◽  
Krzysztof Kutak
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Invariance ◽  
Arbitrary Number ◽  
Gauge Invariant

Abstract We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.

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