Related papers: Path Integrals in Polar Field Variables in QFT
In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with quartic potentials. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
Using the notion of distribution on an infinite dimensional space defined in our previous paper, we give definition of a version of dynamical evolution in quantum field theory, motivated by heuristic formulas involving path integrals.
In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…
The quaternion Fourier transform (QFT), a generalization of the classical 2D Fourier transform, plays an increasingly active role in particular signal and colour image processing. There tends to be an inordinate degree of interest placed on…
In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…
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.
We show how Gravitational Path Integral formulae for various quantities that have been computed in the literature, follow from a few coarse grained hydrodynamic assumptions about the relations between space-time geometry, entropy, and…
The identification of physical degrees of freedom is sometimes obscured in the path integral formalism, and this makes it difficult to impose some constraints or to do some approximations. I review a number of cases where the difficulty is…
We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. We also…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
The electrostatic configurations of the Born-Infeld field in the 2-dimensional Euclidean plane are obtained by means of a non-analytical complex mapping which captures the structure of equipotential and field lines. The electrostatic field…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem…
In the present paper we study the Faddeev-Popov path integral quantization of electrodynamics in an inhomogenious dielectric medium. We quantize all polarizations of the photons and introduce the corresponding ghost fields. Using the heat…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
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.
We construct the path integral formulation of the partition function for a free scalar thermal field theory using coherent states, first in the ladder operator basis and then in the field operator basis. In so doing, we provide for the…