Os efeitos das condições de contorno na eletrodinâmica escalar e o efeito Casimir para N regiões de largura finita e diferentes potenciais - Dilem, Bernardo Brunoro (2012)
The present work can be divided into two main parts: the former, Chapter 3, we have investigated in what conditions the imposition of homogeneous Neumann boundary conditions on two infinite parallel plane surfaces separated by a distance a, could inhibit the spontaneous symmetry breaking in Coleman-Weinberg mechanism for the scalar electrodynamics. In the work of reference [1], this objective has been achieved through an expansion of the effective potential in powers of a?, where ? 2 represents the quadratic terms in the scalar field, from which the critical points ??c? of Vef (maximum and minimum) were found. That approach is tedious and complex, and require careful analyse. In this work, without resorting to any expansion of the effective potential, we have showed in a very simple way that, if a ˜ e 2M-1 ? (where e is the charge of the scalar field and M? its mass generated by Coleman-Weinberg mechanism), ??c? = 0 is the minimum point of Vef and that, therefore, the spontaneous symmetry breaking is inhibited. In the second part, Chapter 6, we have developed a more general proposal to deal with the Casimir effect. As a prototype we have used the real scalar field interacting with N regions of different potentials – represented by step functions – in (n+1) dimensions. As result we have obtained expressions which permit us to calculate, through the momentumenergy tensor, the energy and the force of Casimir for any number of barriers or regions of different constant potentials, consequently it is applicable to very different cases. In the Chapter 7 and 8 we have investigated some possibilities, alternating our original propose of different finite regions and the extreme case of barriers represented by delta Dirac functions. We have also shown that, in the limit of strong coupling, our results recover the famous L¨ucher et al. result, as it was expected