Related papers: The Feynman Propagator from a Single Path
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may…
We propose a classical simulation method for quantum circuits based on decomposing unitary gates into a sum of stabilizer projectors. By only decomposing the non-Clifford gates, we take advantage of the Gottesman-Knill theorem and build a…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman propagator of a particle quantum mechanically moving under a time…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which…
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…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
In this paper, we correct an inaccurate result of previous works on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime, and we derive the generalized analytic formulas of both the scalar Feynman…
It is shown that Feynman's derivation of Maxwell equations admits a generalization to the case of extra spatial dimensions. The generalization is unique and is only possible in seven dimensional space.
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
The Feynman-Garrod path integral representation for time evolution is extended to arbitrary one-parameter continuous canonical transformations. One thereupon obtains a generalized Kerner-Sutcliffe formula for the unique quantum…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
A generalized Feynman Checkerboard model is constructed using a 4-dimensional HyperDiamond lattice. The resulting phenomenological model is the D4-D5-E6 model described in hep-ph/9501252 and quant-ph/9503009.
Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path…