A new approach is presented for the study of the probability that the random paths generated by two independent Brownian motions in ℝd intersect or, more generally, are within a short distance a of each other. The well known behavior of that function of a-above, below, and at the critical dimension d=4, as well as further corrections, are derived here by means of a single renormalization group equation. The equation's derivation is expected to shed some light on the β-function of the λφd4 quantum field theory.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics