A QUATERNIONIC APPROACH TO THE FERMIONIC CASIMIR EFFECT

Raúl Castillo P. and Vladislav V. Kravchenko
Departamento de Telecomunicaciones
Escuela Superior de Ingeniería Mecánica y Eléctrica
Instituto Politécnico Nacional
Av. IPN s/n, Colonia Lindavista, C. P. 07738, D. F. México
Teléfono: 57 29 6000 Ext. 54782
Correo electrónico: raulcastillop@hotmail.com
vkravche@maya.esimez.ipn.mx

The Casimir effect is a small attractive force which acts between two close parallel uncharged conducting plates in a vacuum. It is due to quantum vacuum fluctuations of virtual particles. The effect was predicted by the Hendrick Casimir [1], in 1948 (see also [2], [3], [4], [5]). The model for the fermionic Casimir effect reduces to the following boundary value problem (see e.g. [6], [7]):

[–wg0 + ig×Ñ – m]y = 0 (1)

where w and m are the frequency and the mass of the particle respectively, g is the vector of Dirac matrices g = (g1, g2, g3). The following condition holds at the two infinite plates, which constitute the boundary G:

(2)

where is the unit outward normal to the boundary. This condition not only is compatible with the Dirac equation but also satisfies the natural requirement that the current of particles across the boundary must vanish, according to the so-called MIT bag model, proposed in [8, 9]. Using the quaternionic approach to this model [10] we describe the complete set of modes satisfying the boundary conditions.

References

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