Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

2016

Int. J. Mod. Phys. A

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I investigate the finite temperature Casimir effect for a charged and massless scalar field satisfying mixed (Dirichlet-Neumann) boundary conditions on a pair of plane parallel plates of infinite size. The effect of a uniform magnetic field, perpendicular to the plates, on the Helmholtz free energy and Casimir pressure is studied. The ζ-function regularization technique is used to obtain finite results. Simple analytic expressions are obtained for the zeta function and the free energy, in the limits of small plate distance, high temperature and strong magnetic field. The Casimir pressure is obtained in each of the three limits and the situation of a magnetic field present between and outside the plates, as well as that of a magnetic field present only between the plates is examined. It is discovered that, in the small plate distance and high temperature limits, the repulsive pressure is less when the magnetic field is present between the plates but not outside, than it is when the magnetic field is present between and outside the plates.

“…(27) is within 0.2 percent of the exact value for √ eBa ≥ 2 and √ eB/T ≥ 2, with an accuracy similar to that of Eqs. (21) and (22).…”

Section: Discussionmentioning

confidence: 99%

Section: Strong Magnetic Fieldmentioning

confidence: 99%

Section: Casimir Pressurementioning

confidence: 99%

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Magnetic field corrections to the repulsive Casimir effect at finite temperature

2016

Int. J. Mod. Phys. A

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“…Once we compare Eq. (40) to the well known result for the Weisskopf Lagrangian [30,31], we realize that we must take the arbitrary parameter µ = M , and we'll do that in all our results containing µ. We evaluateζ(s) by using…”

Section: Zeta Function Evaluationmentioning

confidence: 99%

“…(57) where the dominant term is the one-loop vacuum effective potential for scalar QED [31], proportional to the volume of the slab. If we set M = 0 in (57), we reproduce the result of Ref.…”

Section: Free Energy and Casimir Pressurementioning

confidence: 99%

Finite temperature Casimir effect for massive scalars in a magnetic field

Seltzer

2014

Int. J. Mod. Phys. A

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The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass, and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.

Finite temperature Casimir effect for charged massless scalars in a magnetic field

Seltzer

2013

Phys. Rev. D

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The zeta function regularization technique is used to study the finite temperature Casimir effect for a charged and massless scalar field confined between parallel plates and satisfying Dirichlet boundary conditions at the plates. A magnetic field perpendicular to the plates is included. Three equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature and plate distance. These expressions of the zeta function are used to calculate the Helmholtz free energy of the scalar field and the pressure on the plates, in the case of high temperature, small plate distance and strong magnetic field. In all cases, simple analytic expressions are obtained for the free energy and pressure which are accurate and valid for practically all values of temperature, plate distance and magnetic field.