scholarly journals RADIATIVE PROPERTIES OF THE STUECKELBERG MECHANISM

2008 ◽  
Vol 23 (05) ◽  
pp. 741-748 ◽  
Author(s):  
T. J. MARSHALL ◽  
D. G. C. MCKEON
Keyword(s):  
Vector Field ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Radiative Properties ◽  
Loop Order ◽  
Gauge Invariant ◽  
Scalar Quantum

We examine the mechanism for generating a mass for a U(1) vector field introduced by Stueckelberg. First, it is shown that renormalization of the vector mass is identical to the renormalization of the vector field on account of gauge invariance. We then consider how the vector mass affects the effective potential in scalar quantum electrodynamics at one-loop order. The possibility of extending this mechanism to couple, in a gauge invariant way, a charged vector field to the photon is discussed.

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 SUPER-τ3QED AND THE DIMENSIONAL REDUCTION OF N=1SUPER-QED2+2

1996 ◽  
Vol 11 (08) ◽  
pp. 1367-1389 ◽  
Author(s):  
M.A. DE ANDRADE ◽  
O.M. DEL CIMA
Keyword(s):  
Vector Field ◽  
Imaginary Part ◽  
Gauge Invariance ◽  
Dimensional Reduction ◽  
Complex Vector ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Supersymmetric Version ◽  
Supersymmetric Gauge ◽  
Weyl Symmetry

In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .

scholarly journals Two-loop renormalisation of gauge theories in 4D implicit regularisation and connections to dimensional methods

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
A. Cherchiglia ◽  
D. C. Arias-Perdomo ◽  
A. R. Vieira ◽  
M. Sampaio ◽  
B. Hiller
Keyword(s):  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Background Field ◽  
Field Method ◽  
Loop Order ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Lorentz Algebra ◽  
Background Field Method

AbstractWe compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.

scholarly journals THE EFFECTIVE POTENTIAL IN THE MASSIVE $\phi_4^4$ MODEL

2007 ◽  
Vol 22 (01) ◽  
pp. 1-9 ◽  
Author(s):  
F. BRANDT ◽  
F. CHISHTIE ◽  
D. G. C. MCKEON
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Massless Scalar ◽  
Group Equation ◽  
Scalar Quantum ◽  
Text Model

By applying the renormalization group equation, it has been shown that the effective potential V in the massless [Formula: see text] model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive [Formula: see text] model, showing that the effective potential is independent of ϕ here as well.

GAUGE-INVARIANT FORMULATION OF QUANTUM ELECTRODYNAMICS

1955 ◽  
Vol 33 (11) ◽  
pp. 650-660 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Coulomb Field ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Invariant Formulation ◽  
Invariant Operation ◽  
General Gauge

Electrodynamics is formulated so as to be manifestly invariant under general gauge transformations, through being built up entirely in terms of gauge-invariant dynamical variables. The quantization of the theory can be carried out by the usual rules and meets with the usual difficulties.It is found that the gauge-invariant operation of creation of an electron involves the simultaneous creation of an electron and of the Coulomb field around it. The requirement of manifest gauge invariance prevents one from using the concept of an electron separated from its Coulomb field.

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.

scholarly journals Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Qiang Chen ◽  
Jianyuan Xiao ◽  
Peifeng Fan
Keyword(s):  
Field Theory ◽  
Real Time ◽  
Quantum Electrodynamics ◽  
Symplectic Form ◽  
Strong Field ◽  
Relativistic Quantum ◽  
High Order ◽  
High Quality ◽  
Geometric Structures ◽  
Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

GAUGE INVARIANCE AND CONSTRAINTS: OPEN GAUGE ALGEBRAS

1992 ◽  
Vol 07 (22) ◽  
pp. 5549-5561 ◽  
Author(s):  
KH. S. NIROV ◽  
P.N. PYATOV ◽  
A.V. RAZUMOV
Keyword(s):  
Wide Class ◽  
Gauge Invariance ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant

For a wide class of gauge-invariant systems with open gauge algebras the Hamiltonian description is constructed and the Poisson brackets of the constraints are calculated. It is shown that in the case under consideration there arise only first class constraints.

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