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An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass

In this paper we draw attention to the fact that the studies by V. G. Kadyshevsky devoted to the creation of the which \emph{\emph{to the geometric quantum field theory with a fundamental mass}} containing non-Hermitian mass extensions. It is important that these ideas recently received a powerful development in the form of construction of the non-Hermitian algebraic approach. The central point of these theories is the construction of new scalar products in which the average values of non-Hermitian Hamiltonians are valid. Among numerous works on this subject may be to allocate as purely mathematical and containing a discussion of experimental results. In this regard, we consider as the development of algebraic relativistic pseudo-Hermitian quantum theory with a maximal mass and experimentally significant investigations are discussed