Related papers: Path Integration for the Plane Pendulum with Finit…
The universal amplitude ratio $\tilde{R}_{\xi}$ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model for q<4.
We compare expressions for the atom interferometer phase obtained using the path integral approach and the approach based on the density matrix equation in the Wigner representation. The power series of these expressions over the Planck…
We present several results on the geometry of the quantum projective plane CP2q. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles…
The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time. It has been shown that canonical and path-integral approaches may yield different results,…
Recently, the properties of a binomial sum related to the multi-link inverted pendulum enumeration problem have been studied. In this note, we establish bounds for this binomial sum.
In this article a description is given of the measure in Euclidean path-integral in quantum gravity, and recent results using the Faddeev-Popov method of gauge fixing. The results suggest that the effective action is finite and positive.
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced…
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw.
We present a calculation of the planar two-loop five-gluon amplitudes. The amplitudes are obtained in a variant of the generalized unitarity approach suitable for numerical computations, which we extend for use with finite field…
The article provides the formula for the calculation the falling time of inverted pendulum. The result is expressed in terms of elliptic integrals of first kind. The asymptotic formula for small initial inclination value is also provided.
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
I address and solve the natural problem of calculating the transverse current anomalies in quantum electrodynamics by means of the path-integral method. An explicitly divergent and regulator-dependent anomaly term is produced for the vector…
We present the transition amplitude for a particle moving in a space with two times and D space dimensions having a Sp(2,R) local symmetry and an SO(D,2) rigid symmetry. It was obtained from the BRST-BFV quantization with a unique gauge…
Three current models of QCD in (1+1) dimensions are examined and extended in light-front coordinates. A pion of high momentum is found to have an infinite extent along its direction of motion.
Most quantum field theories are not exactly solvable. In this paper show the statistical equivalence of the standard exponential path integral to products of Heaviside functions, i.e. a product of specially tuned uniform distributions. This…
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.
The path-integral approach to cosmology consists in the computation of transition amplitudes between states of the quantum geometry of the universe. In the past, the concrete computation of these transitions amplitudes has been performed in…
Searching for infrastructure of the quantum mechanical system, we study trajectories of the s-wave poles of the S-matrix element with respect to a real phase $\alpha$ in the complex momentum plane for a complex extension of real potentials…
We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…