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Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
The strong coupling between the spatial and polarisation degrees of freedom (DoF) in vector modes enables a diverse array of exotic, inhomogeneous polarisation distributions through a non-separable superposition, which are conventionally…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…
Light transport in graded index media follows a curved trajectory determined by the Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the…
Based on the Sum-over-Paths approach of Richard Feynman, an integration method for calculating wave phase vectors is derived. The diffraction and interference patterns of various slit masks can be calculated from such phase vectors. The…
A new formalism of beam-optics and polarization has been recently presented, based on an exact matrix representation of the Maxwell equations. This is described in Part-I and Part-II. In this Part, we present the application of the above…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
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…
Recently, there has been a revival of interest in mechanisms for changing the spin polarization of an electron beam on transmission through, or reflection from, a magnetic surface. An understanding of these mechanisms would allow the use of…
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role…