Wigner-Moyal description of free variable mass Klein-Gordon fields

Probability Interpretation for Klein-Gordon Fields

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-Gordon fields without having to restrict to the subspaces of the positive-frequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequence...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂2 t +D)ψ(t) = 0, where t ∈ R and D is a positive-definite operator acting in a Hilbert space H̃. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish t...

Position Operators, and Localized States of Klein-Gordon Fields

We construct a concrete realization of the generalized parity (P), time-reversal (T ), and charge-conjugation (C) operators, that were initially defined in the study of the PT symmetric and pseudo-Hermitian Hamiltonians, for Klein-Gordon fields. We show that PT and C operators, that signify certain symmetries of the system, correspond to the ordinary time-reversal and charge-conjugation transfo...

Dirac and Klein – Gordon particles in complex Coulombic fields

The observation that the existence of the amazing reality and discreteness of the spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic potentials are considered. In one of the first explicit studies of the non-Hermitian Schrödinger Hamiltonians, Caliceti et al ...