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Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
Ali Mostafazadeh
We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian opera…
Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
Ali Mostafazadeh
We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solution…
Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians
Ali Mostafazadeh
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensi…
Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology
Ali Mostafazadeh
We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein…
On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension
Ali Mostafazadeh
For a given standard Hamiltonian H=[p-A(x)]^2/(2m)+V(x) with arbitrary complex scalar potential V and vector potential A, with x real, we construct an invertible antilinear operato…
On a Factorization of Symmetric Matrices and Antilinear Symmetries
Ali Mostafazadeh
We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a un…