Related papers: Path Integral for Relativistic Equations of Motion
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…
A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method.…
The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
The path integral for relativistic spinless dionium atom is solved, and the energy spectra are extracted from the resulting amplitude.
The path integral of the relativistic Coulomb system is solved, and the wave functions are extracted from the resulting amplitude.
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the…
In my textbook on Quantum Field Theory \cite{tpqft} and in a recent paper \cite{tpejc2018}, I advocated a lattice regularization procedure for defining the path integral for the relativistic particle, using the non-quadratic action…
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action…
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov…
The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears,…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We discuss the formulation of spin observables associated to a non-relativistic spinning particles in terms of grassmanian differential operators. We use as configuration space variables for the pseudo-classical description of this system…