0 Rigorous Real - Time Feynman Path Integral for Vector Potentials
نویسندگان
چکیده
Abstract. In this paper, we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the L transition probability amplitude via improper Riemann integrals. Our formulation will hold for vector potential Hamiltonian for which its potential and vector potential each carries at most a finite number of singularities and discontinuities.
منابع مشابه
A Rigorous Real Time Feynman Path Integral and Propagator
Abstract. We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic L transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite num...
متن کاملA Rigorous Real Time Feynman Path Integral
where φ, ψ ∈ L, H = −~ 2m ∆+V (~x) is essentially self-adjoint, H̄ is the closure ofH , and φ, ψ, V each carries at most a finite number of singularities and discontinuities. In flavor of physics literature, we will formulate the Feynman path integral with improper Riemann integrals. In hope that with further research we can formulate a rigorous polygonal path integral, we will also provide a No...
متن کاملDiscrete-Time Path Distributions on Hilbert Space
We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials.
متن کاملExtended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method
We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than pr...
متن کاملBayesian Approach to Inverse Quantum Statistics: Reconstruction of Potentials in the Feynman Path Integral Representation of Quantum Theory
The Feynman path integral representation of quantum theory is used in a non–parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator, and th...
متن کامل