Coleman–Weinberg potential
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Coleman–Weinberg potential
Coleman–Weinberg potential
The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is
where the scalar field is complex,is the electromagnetic field tensor, andthe covariant derivative containing the electric chargeof the electromagnetic field.
Assume thatis nonnegative. Then if the mass term is tachyonic,there is aspontaneous breakingof thegauge symmetryat low energies, a variant of theHiggs mechanism. On the other hand, if the squared mass is positive,the vacuum expectation of the fieldis zero. At the classical level the latter is true also if. However, as was shown bySidney ColemanandErick Weinbergeven if the renormalized mass is zero spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - model have aconformal anomaly).
The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar fieldwill manifest themselves as a naturally lightHiggs boson, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter thanvector bosons. There are non-minimal models that give a more realistic scenarios. Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries includingsupersymmetry.
Equivalently one may say that the model possesses a first-orderphase transitionas a function of. The model is the four-dimensional analog of the three-dimensionalGinzburg–Landau theoryused to explain the properties ofsuperconductorsnear thephase transition.
The three-dimensional version of the Coleman–Weinberg model governs the superconducting phase transition which can be both first- and second-order, depending on the ratio of theGinzburg–Landau parameter, with atricritical pointnearwhich separatestype Ifromtype IIsuperconductivity.
Historically, the order of the superconducting phase transition was debated for a long time since the temperature
interval where fluctuations are large (Ginzburg interval) is extremely small.
The question was finally settled
in 1982.[1] If the Ginzburg-Landau parameterthat distinguishestype-Iandtype-IIsuperconductors (see alsohere)
is large enough, vortex fluctuations
becomes important
which drive the transition to second order.
The tricritical point lies at
roughly, i.e., slightly below the valuewheretype-Igoes over intotype-IIsuperconductor.
The prediction was confirmed in 2002 byMonte Carlo computer simulations.[2]
Literature
S. Coleman and E. Weinberg (1973). "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking". Physical Review D. 7 (6): 1888–1910. arXiv:hep-th/0507214 [6] . Bibcode:1973PhRvD...7.1888C [7] . doi:10.1103/PhysRevD.7.1888 [8] .
L.D. Landau (1937). Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki. 7: 627. Missing or empty |title= (help)
V.L. Ginzburg and L.D. Landau (1950). Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki. 20: 1064. Missing or empty |title= (help)
M.Tinkham (2004). Introduction to Superconductivity. Dover Books on Physics (2nd ed.). Dover. ISBN 0-486-43503-2.
References
[1]
Citation Link//doi.org/10.1007%2FBF02754760H. Kleinert (1982). "Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition" (PDF). Lettere al Nuovo Cimento. 35 (13): 405–412. doi:10.1007/BF02754760.
Oct 1, 2019, 4:47 PM
[2]
Citation Link//doi.org/10.1103%2FPhysRevB.66.064524J. Hove; S. Mo; A. Sudbo (2002). "Vortex interactions and thermally induced crossover from type-I to type-II superconductivity" (PDF). Phys. Rev. B 66 (6): 064524. arXiv:cond-mat/0202215. Bibcode:2002PhRvB..66f4524H. doi:10.1103/PhysRevB.66.064524.
Oct 1, 2019, 4:47 PM
[9]
Citation Linkwww.physik.fu-berlin.de"Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition"
Oct 1, 2019, 4:47 PM
[11]
Citation Linkwww.physik.fu-berlin.de"Vortex interactions and thermally induced crossover from type-I to type-II superconductivity"
Oct 1, 2019, 4:47 PM
[15]
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Oct 1, 2019, 4:47 PM