Related papers: Remarks on the Origin of Path Integration: Einstei…
In classical mechanics matter and fields are completely separated. Matter interacts with fields. For particle physicists this is not the case. Both matter and fields are represented by particles. Fundamental interactions are mediated by…
The unification of gravity and quantum mechanics remains one of the most profound open questions in science. With recent advances in quantum technology, an experimental idea first proposed by Richard Feynman is now regarded as a promising…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering…
The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
This essay gives a short, informal account of the development of digital logic from the Pleistocene to the Manhattan Project, the introduction of reversible circuits, and Richard Feynman's allied proposal for quantum computing. We argue…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a…
It is shown that Non-unitary Newtonian Gravity (NNG) model admits a simple interpretation in terms of Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between…
We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman path integral expression for the Feynman propagator of aparticle quantum mechanically moving under an external…
Using the example of classical electrodynamics, I argue that the concept of fields as mediators of particle interactions is fundamentally flawed and reflects a misguided attempt to retrieve Newtonian concepts in relativistic theories. This…
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on…
In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical…
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.
A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…