scholarly journals Gauge invariance of the one-loop effective action of the Higgs field in the SU(2) Higgs model

1999 ◽  
Vol 60 (10) ◽  
Author(s):  
Jürgen Baacke ◽  
Katrin Heitmann
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Higgs Field ◽  
Higgs Model ◽  
The One

scholarly journals Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1237
Author(s):  
Dmitry Antonov
Keyword(s):  
Gauge Boson ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Higgs Model ◽  
Analytic Calculation ◽  
Standard Result ◽  
Correlation Lengths ◽  
Yang Mills ◽  
Diamagnetic Contribution ◽  
The One

We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

PHASE TRANSITIONS IN THE ABELIAN HIGGS MODEL AT FINITE DENSITIES

1991 ◽  
Vol 06 (23) ◽  
pp. 4063-4076 ◽  
Author(s):  
V.J. PETER ◽  
M. SABIR
Keyword(s):  
Phase Transitions ◽  
Density Dependence ◽  
Gauge Invariance ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Higgs Model ◽  
Coupling Constants ◽  
Abelian Higgs Model ◽  
Multiple Phase ◽  
The One

We study the U(1)-invariant Abelian Higgs model at a finite temperature and a finite chemical potential, at the one-loop level of approximation, and show the existence of chemical-potential-induced multiple-phase transitions at finite temperatures. The temperature and density dependence of the coupling constants is also analyzed. The gauge invariance of the results obtained is demonstrated.

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 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.

OPERATOR REGULARIZATION AND THE DIVERGENCE OF THE SUPERCURRENT

1987 ◽  
Vol 02 (03) ◽  
pp. 785-796 ◽  
Author(s):  
D. G. C. McKEON ◽  
T. N. SHERRY
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Green's Functions ◽  
Green’S Functions ◽  
Perturbative Expansion ◽  
Feynman Diagrams ◽  
Spinor Particle ◽  
Yang Mills ◽  
Loop Level ◽  
The One

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the ζ-function. A perturbative expansion due to Schwinger allows one to compute from the ζ-function one-loop one-particle irreducible Green's functions. By regulating in this way, we do not have to compute Feynman diagrams, we avoid having to introduce a regulating parameter into the initial Lagrangian and we do not encounter any divergent integrals. This procedure is illustrated for N = 1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the super-current is recovered.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

scholarly journals NONPERTURBATIVE FIELD CORRELATOR AND STRING REPRESENTATION FOR THE 't HOOFT LOOP AVERAGE IN THE ABELIAN HIGGS MODEL

1998 ◽  
Vol 13 (09) ◽  
pp. 659-671 ◽  
Author(s):  
D. V. ANTONOV
Keyword(s):  
Field Strength ◽  
Higgs Field ◽  
Exact Result ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
String Tension ◽  
Higgs Model ◽  
Effective Theory ◽  
Abelian Higgs Model ◽  
String Representation

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs model string representation for the 't Hooft loop average defined on the string worldsheet, which yields the values of two coefficient functions parametrizing the bilocal correlator of the dual field strength tensors. The asymptotic behaviors of these functions agree with the ones obtained within the method of vacuum correlators in QCD in the lowest order of perturbation theory. We demonstrate that the bilocal approximation to the method of vacuum correlators is an exact result in the Londons' limit, i.e. all the higher cumulants in this limit vanish. We also show that at large distances, apart from the integration over metrics, the obtained string effective theory (which in this case reduces to the nonlinear massive axionic sigma model) coincides with the low energy limit of the dual version of 4D compact QED, the so-called universal confining string theory. We derive string tension of the Nambu–Goto term and the coupling constant of the rigidity term for the obtained string effective theory and demonstrate that the latter is always negative, which means the stability of strings, while the positiveness of the former is confirmed by the present lattice data. These data enable us to find the Higgs boson charge and the vacuum expectation value of the Higgs field, which well-described QCD. We also study dynamics of the weight factor of the obtained string representation for the 't Hooft average in the loop space. In conclusion, we obtain string representation for the partition function of the correlators of an arbitrary number of Higgs currents, by virtue of which we rederive the structure of the bilocal correlator of the dual field strength tensors, which yields the surface term in the string effective action.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

2021 ◽  
pp. 2150142
Author(s):  
David Montenegro ◽  
B. M. Pimentel
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Mass Shell ◽  
Natural Extension ◽  
Quantum Model ◽  
Covariant Quantization ◽  
Heisenberg Picture ◽  
Maxwell Electrodynamics ◽  
Loop Amplitude ◽  
The One

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

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