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, and the covariant derivative containing the electric charge of the electromagnetic field. The model illustrates the generation of mass by fluctuations of the vector field. Equivalently one may say that the model possesses a first-order phase transition as a function of . The model is the four-dimensional analog of the three-dimensional Ginzburg-Landau Theory used to explain the properties of superconductors near the phase transition. Interestingly, the three-dimensional version of the Coleman-Weinberg model has both a first and a second-order phase transition depending on the ratio of the Ginzburg-Landau parameter , with a
tricritical point near which separates type I from type II superconductivity.
References
*S. Coleman and E. Weinberg, Phys. Rev. D7, 1888 (1973). [http://prola.aps.org/abstract/PRD/v7/i6/p1888_1]
*L.D. Landau, Zh. Elsp. Teor. Fiz. 7, 627 (1937).
*V.L. Ginzburg and L.D. Landau, ibid. 20, 1064 (1950).
*cite book | author=Michael Tinkham | title=Introduction to Superconductivity | edition = 2nd ed. | publisher=Dover Books on Physics | year=2004 | id=ISBN 0-486-43503-2 (Paperback)
*Hagen Kleinert, Lett. Nuovo Cimento {f 35}, 405 (1982) (http://www.physik.fu-berlin.de/~kleinert/97/97.pdf).
*Hagen Kleinert, "Gauge Fields in Condensed Matter", Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1--742, Vol. II, "STRESSES AND DEFECTS", pp. 743-1456, [http://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)] ; Paperback ISBN 9971-5-0210-0 " (also available online: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html Vol. I] and [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents2.html Vol. II] )"
*Hagen Kleinert, "Limitations on Coleman-Weinberg Mechanism", Phys. Lett. B 128, 69 (1983) (http://www.physik.fu-berlin.de/~kleinert/106/106.pdf).
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