Related papers: Path Integral on Relativistic Spinless Potential P…
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…
We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
Approximate analytic solutions of the Dirac equation with Tietz-Hua (TH) potential are obtained for arbitrary spin-orbit quantum number using the Pekeris approximation scheme to deal with the spin-orbit coupling terms In the presence of…
We explore a new approach to the path integral for a latticized quantum theory. This talk is based on work with N. Khuri and H. Ren.
Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized…
Although Potent purports to use only radial velocities in reconstructing the potential velocity field of galaxies, the derivation of transverse components is implicit in the smoothing procedures adopted. Thus the possibility arises of using…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of…
The spin 1 particle is treated in the presence of the Dirac magnetic monopole in the Minkowski and Lobachevsky spaces. Separating the variables in the frame of the matrix 10-component Duffin-Kemer-Petiau approach (wave equation) and making…
The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(\omega x)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for…
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…
The path integral on the single-sheeted hyperboloid, i.e.\ in $D$-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call ``Kepler-problem'', and the case of a constant magnetic field are also discussed.
We present a systematic approach for the separation of variables for the two-dimensional Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac spinor via minimal coupling, along with the scalar potential…
We provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann-Liouville fractional elliptic problems on a finite domain. The boundedness and stability analysis of the…
We propose an alternative method for Feynman path integrals on compact Riemannian manifolds. Our method employs action integrals along the shortest paths. In the case of rank 1 locally symmetric Riemannian manifolds, we prove the strong…
The solubility of a general two dimensional model, which reduces to various models in different limits, is studied within the path integral formalism. Various subtleties and interesting features are pointed out.