Non-hermitian PT-symmetric theories

This dissertation concerns the concept of PT symmetry as a replacement of the conventional symmetry of the Dirac Hermiticity of the operators, in particular, for the Hamiltonian. After solving a controversial issue surrounding the claimed violation of the special relativity by PT-symmetric quantum mechanics, we move further to discuss PT symmetry for the systems whose associated time reversal symmetry is odd, i.e., T${}^2$ = -1. Our results, as published papers, are incorporated in the subsequent chapters. Then we conclude by suggestions for future work.