相关论文: Source Driven Solutions of Quantum Field Theories
In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the…
In this work, approximate solutions to the nonlinear Klein-Gordon equation are constructed by means of the Galerkin method. Specifically, it is shown how the dynamics of a real scalar field in $1+1$ dimensions subjected to Dirichlet…
The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. The approach is based on the…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more…
These lecture notes introduce the Galerkin method to approximate solutions to partial differential and integral equations. We begin with some analysis background to introduce this method in a Hilbert Space setting, and subsequently…
We use a concept of weak asymptotic solution for homogeneous as well as non-homogeneous fractional advection dispersion type equations. Using Legendre scaling functions as basis, a numerical method based on Galerkin approximation is…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires…
Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the…
In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin…
We couple the L1 discretization for Caputo derivative in time with spectral Galerkin method in space to devise a scheme that solves quasilinear subdiffusion equations. Both the diffusivity and the source are allowed to be nonlinear…
We present a precise solution of the polaron problem by a novel Monte Carlo method. Basing on conventional diagrammatic expansion for the Green function of the polaron, $G({\bf k}, \tau)$, we construct a process of generating continuous…
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
A quantum field theory formalism is reviewed that leads to a self-consistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
We develop and analyse a numerical method for the time-fractional nonlocal thermistor problem. By rigorous proofs, some error estimates in different contexts are derived, showing that the combination of the backward differentiation in time…