Position Operators, and Localized States of Klein-Gordon Fields
نویسنده
چکیده
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 transformations, respectively. Furthermore, we construct a positive-definite and relativistically invariant inner product on the space of Klein-Gordon fields and show that the generator h of time-translations viewed as acting in the Hilbert space H defined by this inner product is Hermitian. The quantum system having H as its Hilbert space and h as its Hamiltonian is unitarily equivalent to the one defined by a Hermitian Hamiltonian acting in the Hilbert space L2(R3) ⊕ L2(R3). We give the explicit form of the corresponding unitary transformation and use it to construct position operators, localized and coherent states, and a set of wave functions for the KleinGordon fields. Our approach provides a consistent quantum mechanical description of the Klein-Gordon fields that admits a genuine probabilistic interpretation. ∗E-mail address: [email protected]
منابع مشابه
A Physical Realization of the Generalized PT -, C-, and CPT -Symmetries and the Position Operator for Klein-Gordon Fields
Generalized parity (P), time-reversal (T ), and charge-conjugation (C) operators were initially defined in the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show that in this realization PT and C operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a...
متن کاملSoliton-like Solutions of the Complex Non-linear Klein-Gordon Systems in 1 + 1 Dimensions
In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...
متن کاملAnalytical solutions for the fractional Klein-Gordon equation
In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.
متن کاملNumerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods
متن کامل
B-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION
We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.
متن کامل