beta functions of a scalar theory coupled to gravity.
We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.
Renormalization-group flow of the dilaton potential.
We consider a scalar-metric gauge theory of gravity with independent metric, connection and dilaton. The role of the dilaton is to provide the scale of all masses, via its vacuum expectation value. In this theory, we study the renormalization group flow of the dilaton potential, taking into account threshold effects at the Planck scale. Due to the running of the VEV of the dilaton all particles that would naively seem to have masses larger than Planck's mass, may actually not propagate. This could solve the problem of unitarity in these theories.
The quantum particle in a box: what we can learn from classical electrodynamics
The problem of a charged particle enclosed in an infinite square potential well is analysed from the point of view of classical theory with the addition of the electromagnetic zero-point radiation field, with the aim to explore the extent to which such an analysis can contribute to enhance our understanding of the quantum behavior. First a proper treatment is made of the freely moving particle subject to the action of the radiation field, involving a frequency cutoff ωc. The jittering motion and the effective structure of the particle are sustained by the permanent action of the zero-point field. As a result, the particle interacts resonantly with the traveling field modes of frequency ωc in its proper frame of reference, which superpose to give rise to a modulated wave accompanying the particle. This is identified with the de Broglie wave, validating the choice of Compton’s frequency for ωc. For the stationary states of particles confined in the potential well, the Lorentz force produced by the accompanying field is shown to lead to discrete values for the mean speed and to an uneven probability distribution that echoes the corresponding quantum distribution. The relevance of the results obtained and the limitations of the classical approach used, are discussed in the context of present-day stochastic electrodynamics.