Boundary conditions in the Unruh problem

Abstract

We have analyzed the Unruh problem in the frame of quantum field theory and have shown that the Unruh quantization scheme is valid in the double Rindler wedge rather than in Minkowski spacetime. The double Rindler wedge is composed of two disjoint regions ($R$- and $L$-wedges of Minkowski spacetime) which are causally separated from each other. Moreover the Unruh construction implies existence of boundary condition at the common edge of $R$- and $L$-wedges in Minkowski spacetime. Such boundary condition may be interpreted as a topological obstacle which gives rise to a superselection rule prohibiting any correlations between $r$- and $l$- Unruh particles. Thus the part of the field from the $L$-wedge in no way can influence a Rindler observer living in the $R$-wedge and therefore elimination of the invisible "left" degrees of freedom will take no effect for him. Hence averaging over states of the field in one wedge can not lead to thermalization of the state in the other. This result is proved both in the standard and algebraic formulations of quantum field theory and we conclude that principles of quantum field theory does not give any grounds for existence of the "Unruh effect".Comment: 31 pages,1 figur

Scalar and fermion representations of the Lorentz group in Minkowski plane, QFT correlators, pair creation in electric field and the Unruh effect

“…Ref. 12. By applying the same projector to a negative frequency plane wave, we obtain the negative energy boost states e …”

“…9 and results in the so-called boost modes 12,21,22 . The boost modes can be also obtained if we take a positive frequency plane wave in the rest frame e −imt and apply to it the projectorΩ κ = δ(B − κ):…”

“…Seemingly, both the origin and horizons (where 'technical' difficulties are observed), being of zero measure in MS, never contribute to 'smeared fields', and hence can be safely ignored 7,8 . In order to check if this is really true, let us consider the fully regularized (in both senses (19) and (20)) zero mode contribution which is supposed to be omitted in the course of the procedure (12). Then, using Eq.…”

“…The integral in Eq. (4) can be reduced 12,23 to cylindrical functions of imaginary index in each of the wedges R, F , L and P of MS, and to Γ-functions at the horizons, cf. Ref.…”

“…Though our presentation is simple and visual, it is rather condensed. Further details can be found in our previous publications [9][10][11][12][13][14][15][16] . For the sake of simplicity, we almost everywhere assume D = 1 + 1 and use the units = c = 1.…”