Proper fluctuations associated with quantum tunneling in field theory

It is shown that, to the lowest order in $\hbar,$ the particle production related to the tunneling that leads to the false vacuum decay is described by the orthogonal part of fluctuation field with respect to the bounce solution. As a simple example the spatially homogeneous tunneling is considered in order to illustrate the consequences coming from such a restriction of the fluctuation field.Comment: Latex, 5 pages, 1 figur

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space-time dimension

A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this paper is twofold. First, we find that box-counting dimension in face of finite resolution of space-time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.Comment: 6 pages, Accepted for publication in Phys. Lett.

Particle production by the expanding thin-walled bubble

Neglecting the effect of particle production at the moment of bubble nucleation, the spectrum of created particles during the bubble expansion is evaluated in the thin-wall approximation. It is shown that the expanding thin-walled bubble makes the dominant contribution to the particle production.Comment: 5 page