Was Polchinski wrong? Colombeau distributional Rindler space-time with distributional Levi-Cività connection induced vacuum dominance. Unruh effect revisited

Abstract

The vacuum energy density of free scalar quantum field Φ in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background spacetime with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Cività connection. In particular we obtain that the vacuum fluctuations 2 have a singular behavior at a Rindler horizon R 0 : 2 4 , as c 2 /a, a . Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski's account doesn't violate of the Einstein equivalence principle.

The Solution Cosmological Constant Problem. Quantum Field Theory in Fractal Space-Time with Negative Hausdorff-Colombeau Dimensions and Dark Matter Nature

“…. , k n 1 , m are infinite large Colombeau generalized numbers [23], [26]. where P i p stands for a polynomial of degree i in the components of p. We can write the denominator of p, k 1 , .…”

“…In fact, the causal Green function of the QFT is the classical Schwartz distribution which is defined on a test smooth functions. It has the δ-function like singularities and needs an additional definition for the product of several such functions at a single point.The discussed above diagram (see Fig.3 [21]- [22], [23]- [26]) there is no any problem arises from the Schwartz Impossibility Theorem.…”

“…Remark 3.2.5.We have aplied now the Colombeau approach [21]- [26] and replaced ill defined formal expression (3.2.1) by well defined Colombeau generalized function [21]- [26]:…”

“…Indeed, the simplest divergent loop diagram (Fig. (see [21][22]) of the Colombeau generalized functions instead classical Schwartz distribution and Colombeau generalized numbers (see [21]- [22], [23]- [26]) there is no any problem arises from the Schwartz Impossibility Theorem.…”

“…Colombeau generalized number[26].In order to eliminate the infinite large Colombeau generalized quantities ln 1 , 1 , respectively from Colombeau integral (3.4.14),i.e., make it finite, we apply Pauli-Villars renormalization via Colombeau generalized functions,see sect.3.2. Finally we get in contrast with canonical formal approuch[8],[33][34][35][36] we cannot taking the limit M PV in (3.4.15) ,see sect.3.2.…”