The model of a domain wall (“thick” brane) in noncompact five-dimensional spacetime is considered with geometries of AdS ₅ type generated by self-interacting scalar matter. The scalar matter is composed of two fields with O(2) symmetric self interaction. One of them is mixed with gravity scalar modes and plays role of the brane formation mode (due to a kink background) and another one is of a Higgs-field type. The interplay between soft breaking of O(2) symmetry and gravity influence is thoroughly investigated around the critical point of spontaneous t symmetry breaking when the v.e.v. of the Higgs-type scalar field occurs. The possibility of (quasi)localization of scalar modes on such thick branes is examined.

The non-Hermitian but $\mathcal{P}\mathcal{T}$-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However, the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this nonlocality affects observable quantities. We consider the case when the intrinsic parity of the interaction terms is determined by degree of coupling constant. We show that the perturbative S matrix of the equivalent Hermitian description can be easily obtained from the perturbative S matrix of the non-Hermitian model. Namely, the first order vanishes whereas the second order is given by the real part of the second order T matrix of the non-Hermitian model. We compute directly the 2-point and 4-point correlation functions in the equivalent Hermitian model for the $i{\varphi }^3$ model and find the results consistent with this relation. The 1-loop correction to the mass happens to be real reflecting the disappearance of 2-body decays. However, the 2 to 2 scattering amplitude obtained using LSZ formula has poles taken in principal value which implies the violation of the causality.

The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum contexts of Wheeler–DeWitt geometrodynamics. In the quantum case of quintessence field with...