Renormalization group and the emergence of random fractal topology in quantum field theory

This work reveals the close connection between the random fractal topology of space–time in microphysics and the renormalization group program (RG) of quantum field theory. As known, the primary goal of RG is to consistently remove divergences from quantum computations by factoring in the energy scale (μ) at which physical processes are probed. RG postulates that the action functional is independent of any particular choice of μ, that is, physical processes are invariant to arbitrary changes of the observation scale. In this context, we conjecture that μ represents a continuous random variable having a uniform density function. Novel results emerge in the basin of attraction of all fixed points, namely: (i) the field exponent becomes a continuous random variable and (ii) space–time coordinates become fractals with random dimensions. It is concluded that the random topology of space–time is not an exclusive attribute of the Planck scale but an inherent manifestation of stochastic dynamics near any fixed point of the underlying field theory.