Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology
نویسنده
چکیده
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 positivefrequency solutions. Our method has a much wider domain of application and may be used to obtain the most general invariant inner-product on the solution space of a broad class of Klein-Gordon type evolution equations. We explore its consequences for the solutions of the Wheeler-DeWitt equation associated with the FRW-massive-realscalar-field models.
منابع مشابه
A Genuine Probability Interpretation for Klein-Gordon Fields and Its Implications for Quantum Cosmology
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 positivefrequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequences...
متن کاملProbability 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...
متن کاملPosition 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...
متن کاملQuantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
We derive an explicit manifestly covariant expression for the most general positivedefinite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities J μ a , with a ∈ (−1, 1), that are analogous to the chiral current density for spin half fields. The conservation of J a is related to...
متن کاملکوانتش گرانش و بررسی هندسی مکانیک کوانتمی
We elaborate on some recent results on a solution of the Hilbert-space problem in minisuperspace quantum cosmology and discuss the consequences of making the (geometry of the) Hilbert space of ordinary nonrelativistic quantum systems time-dependent. The latter reveals a remarkable similarity between Quantum Mechanics and General Relativity.
متن کامل