Dirac's Observables for the Higgs Model I: The Abelian Case

We search a canonical basis of Dirac's observables for the classical Abelian Higgs model with fermions in the case of a trivial U(1) principal bundle. The study of the Gauss law first class constraint shows that the model has two disjoint sectors of solutions associated with two physically different phases. In the electromagnetic phase, the electromagnetic field remains massless: after the determination of the Dirac's observables we get that both the reduced physical Hamiltonian and Lagrangian are nonlocal. In the Higgs phase, the electromagnetic field becomes massive and in terms of Dirac's observables we get a local, but nonanalytic in the electric charge (or equivalently in the sum of the electromagnetic mass and of the residual Higgs field), physical Hamiltonian; however the associated Lagrangian is nonlocal. Some comments on the R-gauge-fixing, the possible elimination of the residual Higgs field and on the Nielsen–Olesen vortex solution close the paper.

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Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

International Journal of Modern Physics A ◽

10.1142/s0217751x97002553 ◽

1997 ◽

Vol 12 (26) ◽

pp. 4797-4821 ◽

Cited By ~ 6

Author(s):

Luca Lusanna ◽

Paolo Valtancoli

Keyword(s):

Principal Bundle ◽

A Priori ◽

Canonical Basis ◽

Higgs Field ◽

Higgs Model ◽

Gauge Fields ◽

Coupling Constant ◽

Non Local ◽

Two Phases ◽

Higgs Fields

We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given representation of SU(2). Since each one of the three Gauss law first class constraints can be solved either in the corresponding longitudinal electric field or in the corresponding Higgs momentum, we get a priori eight disjoint phases of solutions of the model. The only two phases with SU(2) covariance are the SU(2) phase with massless SU(2) fields and the Higgs phase with massive SU(2) fields. The Dirac observables and the reduced physical (local) Hamiltonian and (non-local) Lagrangian of the Higgs phase are evaluated:the main result is the nonanalyticity in the SU(2) coupling constant, or equivalently in the sum of the residual Higgs field and of the mass of the SU(2) fields. Some comments on the function spaces needed for the gauge fields are made.

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The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽

10.3390/galaxies9010018 ◽

2021 ◽

Vol 9 (1) ◽

pp. 18

Author(s):

Alexander Burinskii

Keyword(s):

Electromagnetic Field ◽

Quantum Theory ◽

Gravitational Field ◽

Dirac Equation ◽

Higgs Field ◽

Vacuum State ◽

Relativistic String ◽

Dirac Equations ◽

Dirac Electron ◽

Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

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The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 2. The weak field approximation in the 3-orthogonal gauges and Hamiltonian post-minkowskian gravity: the N-body problem and gravitational waves with asymptotic background 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

Canadian Journal of Physics ◽

10.1139/p11-101 ◽

2012 ◽

Vol 90 (11) ◽

pp. 1077-1130 ◽

Cited By ~ 11

Author(s):

David Alba ◽

Luca Lusanna

Keyword(s):

Electromagnetic Field ◽

Gravitational Waves ◽

Particle System ◽

Canonical Basis ◽

Field Approximation ◽

Weak Field ◽

N Body Problem ◽

Hamilton Equations ◽

Weak Field Approximation ◽

Tetrad Gravity

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

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

Modern Physics Letters A ◽

10.1142/s0217732398000711 ◽

1998 ◽

Vol 13 (09) ◽

pp. 659-671 ◽

Cited By ~ 13

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.

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Computer and measurement determination of the electromagnetic field parameters. theory and practice

6th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service, 2003. TELSIKS 2003. ◽

10.1109/telsks.2003.1246266 ◽

2004 ◽

Author(s):

E. Grudzinski ◽

V. Nichoga ◽

P. Dub

Keyword(s):

Electromagnetic Field ◽

Theory And Practice

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BRST QUANTIZATION OF GAUGE THEORIES ON THE HYPERSPHERE

Modern Physics Letters A ◽

10.1142/s0217732391002414 ◽

1991 ◽

Vol 06 (24) ◽

pp. 2201-2203 ◽

Cited By ~ 1

Author(s):

D. G. C. McKEON

Keyword(s):

Vector Field ◽

Gauge Field ◽

Gauge Theories ◽

Brst Quantization ◽

Radial Component ◽

Effective Lagrangian ◽

Abelian Case ◽

Gauge Fixing

Drummond and Shore have shown that the most convenient gauge fixing term for gauge theories on a hypersphere is not a perfect square. We show how BRST quantization can be used to generate this gauge fixing term. This involves the introduction of two ghost fields, ci and [Formula: see text], the second of which is an anticommuting vector field. In the Abelian case, only the radial component of [Formula: see text] enters the effective Lagrangian; this is true in the non-Abelian case only if the gauge field is tangential to the hypersphere.

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ЗМІНА ЕЛЕКТРИЧНИХ ВЛАСТИВОСТЕЙ НАСІННЯ ПІД ВПЛИВОМ ВИСОКОЧАСТОТНОГО ЕЛЕКТРОМАГНІТНОГО ОПРОМІНЕННЯ

Вісник Полтавської державної аграрної академії ◽

10.31210/visnyk2014.02.31 ◽

2014 ◽

pp. 151-155

Author(s):

О. М. Петровський

Keyword(s):

Electromagnetic Field ◽

High Frequency ◽

Electric Properties ◽

Electric Resistance ◽

Active Resistance ◽

Exchange Processes ◽

High Frequency Electromagnetic Field ◽

Stimulation Of

Розглянуті питання передпосівної стимуляції на-сіння високочастотним електромагнітним полем.Запропоновано спосіб опромінення насіння і визна-чення його електричних характеристик. На основібудови клітин визначені електричні властивості біо-логічної тканини, з якої складається насіння. Пока-зана зміна складових активного опору в залежностівід частоти струму. Експериментально доведено,що еквівалентну електричну схему неможливо звес-ти до простих випадків з’єднання опорів і ємностей,а саме насіння не можна вважати нейтральнимдіелектриком. Розроблена методика оцінки інтенси-вності обмінних процесів залежно від електричногоопору насіння. The questions of stimulation of seed before sowing are considered by the high-frequency electromagnetic field considered. The method of irradiation of seed and determination of him is offered electric descriptions. On the basis of structure of cages electric properties of biological fabric which seed consist of are certain. The change of constituents of active resistance is shown depending on frequency of current. It is experimentally proved that it is impossible to erect an equivalent electric chart to the simple cases of connection of resistances and capacities, namely seed can not be considered a neutral dielectric. The method of estimation of intensity of exchange processes is developed depending on electric resistance of seed.

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WITHOUT A CONFLICT MODEL OF ELECTRON

10.46813/2019-121-016 ◽

2019 ◽

pp. 16-20

Author(s):

Vasil Tchaban

Keyword(s):

Elementary Particle ◽

Black Hole ◽

Electromagnetic Field ◽

Charge Density ◽

Point Charge ◽

Quark Distribution ◽

Electromagnetic Mass ◽

White Hole ◽

Universal Formula ◽

Conflict Model

The model of electron is oﬀered with quark distribution of charge density and ”white hole” (on similarity of ”black hole” in gravitation) in a center. Such structure abolishes the crisis of electromagnetic mass, calculated on universal formula and on the impulse of the electromagnetic ﬁeld. A model in order to please a classic electrodynamics keeps monolithic nature of elementary particle, and in order to please a quantum allows the separate charged zones to interpret as separate quarks. Coming from harmony of spheres of the separate charged zones, a white hole can be interpreted as white (neutral) quark conditionally in addition to three coloured. As after the electric radius re = 1.185246·10−15 m of white hole the laws of electricity do not operate, then the crisis of point charge is removed at the same time too, because of must be: r ≥ re.

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