The Role of Fermions in Bubble Nucleation

We present a study of the role of fermions in the decay of metastable states of a scalar field via bubble nucleation. We analyze both one and three-dimensional systems by using a gradient expansion for the calculation of the fermionic determinant. The results of the one-dimensional case are compared to the exact results of previous work.Comment: 15 pages, revtex, 9 figure

Resonance, multiple diffusion and critical tunneling for Gaussian lasers

We present a detailed study of the gaussian laser propagation through a dielectric system composed by two right angle prisms. We investigate the transition between the spatial coherence limit, which exhibits wave-like properties and for which the resonance phenomenon can be seen, and the decoherence limit, which exhibits particle-like properties and for which the multiple diffusion occurs. We also analyze the tunneling at critical angles. In our numerical analysis, we shall use BK7 and Fused Silica prisms and a gaussian He-Ne laser with a wavelength of 632.8 nm and beam waists of 2 mm and 200 micron.Comment: 18 pages, 3 tables, 5 figure

The use of the stationary phase method as a mathematical tool to determine the path of optical beams

We use the stationary phase method to determine the path of optical beams which propagate through a dielectric block. In the presence of partial internal reflection, we recover the geometrical result obtained by using the Snell law. For total internal reflection, the stationary phase method overreaches the Snell law predicting the Goos-Haenchen shift.Comment: 11 pages, 2 figure

Semiclassical Series from Path Integrals

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.Comment: 18 pages, 4 figures. References update