scholarly journals Unitary gauge, Stueckelberg formalism, and gauge-invariant models for effective Lagrangians

1993 ◽  
Vol 48 (6) ◽  
pp. 2865-2876 ◽  
Author(s):  
Carsten Grosse-Knetter ◽  
Reinhart Kögerler
Keyword(s):  
Gauge Invariant ◽  
Unitary Gauge ◽  
Stueckelberg Formalism

VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM: GAUGE-INVARIANT REFORMULATION, OPERATOR SOLUTIONS AND HAMILTONIAN AND PATH INTEGRAL FORMULATIONS

2007 ◽  
Vol 22 (39) ◽  
pp. 2993-3001 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Mass Term ◽  
Photon Mass ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Left Handed ◽  
Stueckelberg Formalism ◽  
Massless Fermions

We consider the vector Schwinger model (VSM) describing two-dimensional electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings, with a mass term for the U(1) gauge field and then study its operator solutions and the Hamiltonian and path integral formulations. We emphasize here that although the VSM has been studied in the literature rather widely but only without a photon mass term (which was a consequence of demanding the regularization for the VSM to be gauge-invariant (GI)). The VSM with a photon mass term is seen to be a gauge-noninvariant (GNI) theory. Using the standard Stueckelberg formalism we then construct a GI theory corresponding to the proposed GNI model. From this reformulated GI theory, we further recover the physical contents of the proposed GNI theory under a very special gauge choice. The theory proposed and studied here presents a new class of models in the two-dimensional quantum electrodynamics with massless fermions but with a photon mass term.

A SIMPLE MANNER FOR THE QUANTIZATION OF ANOMALOUS GAUGE THEORIES

1989 ◽  
Vol 04 (05) ◽  
pp. 501-506
Author(s):  
O. J. KWON ◽  
B. H. CHO ◽  
S. K. KIM ◽  
Y. D. KIM
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Quantum Level ◽  
Integral Formalism ◽  
Simple Manner ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Schwinger Model ◽  
Vector Theory ◽  
Stueckelberg Formalism

The chiral Schwinger model is a massive vector theory at the quantum level. We construct the gauge invariant action using Stueckelberg formalism from this. Then the resulting action is exactly the same as the modified action obtained by path-integral formalism. We propose a simple manner for the quantization of anomalous gauge theories.

GAUGE-INVARIANT REFORMULATION OF THE VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM AND ITS HAMILTONIAN, PATH INTEGRAL AND BRST FORMULATIONS

2007 ◽  
Vol 22 (32) ◽  
pp. 6183-6201 ◽  
Author(s):  
USHA KULSHRESHTHA ◽  
D. S. KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Hamiltonian Path ◽  
Mass Term ◽  
Photon Mass ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Gauge Fixing ◽  
Stueckelberg Formalism ◽  
Massless Fermions

Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

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 Mixed NNLO QCD×electroweak corrections of $$ \mathcal{O} $$(Nfαsα) to single-W/Z production at the LHC

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Stefan Dittmaier ◽  
Timo Schmidt ◽  
Jan Schwarz
Keyword(s):  
Z Bosons ◽  
Leading Order ◽  
Current Standard ◽  
Gauge Invariant ◽  
Mass Distributions ◽  
Self Energy ◽  
Electroweak Gauge Boson ◽  
First Results ◽  
Invariant Part ◽  
The Impact

Abstract First results on the radiative corrections of order $$ \mathcal{O} $$ O (Nfαsα) are presented for the off-shell production of W or Z bosons at the LHC, where Nf is the number of fermion flavours. These corrections comprise all diagrams at $$ \mathcal{O} $$ O (αsα) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD×electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at $$ \mathcal{O} $$ O (αsα) are given. Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order $$ \mathcal{O} $$ O (αsα). While the corrections, which are implemented in the Monte Carlo program Rady, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of ≳ 500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.

Gauge-invariant approach and infrared behavior of the spinor propagator

1989 ◽  
Vol 78 (2) ◽  
pp. 185-191 ◽  
Author(s):  
A. N. Sisakyan ◽  
N. B. Skachkov ◽  
I. L. Solovtsov ◽  
O. Yu. Shevchenko
Keyword(s):  
Gauge Invariant ◽  
Infrared Behavior ◽  
Invariant Approach
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