Related papers: A New Approach to Numerical Quantum Field Theory
I outline the basics of numerical solution of quantum field theory using the Source Galerkin method. This method is based on an analysis of the functional differential equations of a field theory in the presence of external sources. This…
The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to…
A new computational idea for continuum quantum field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating…
The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral…
We outline two alternative schemes to perform numerical calculations in quantum field theory. In principle, both of these approaches are better suited to study phase structure than conventional Monte Carlo. The first method, Source…
Some results of the ongoing development of our Source Galerkin (SG) nonperturbative approach to numerically solving Quantum Field theories are presented. This technique has the potential to be much faster than Monte Carlo methods. SG uses…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo…
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual…
The great majority of algorithms employed in the study of lattice field theory are based on Monte Carlo's importance sampling method, i.e. on probability interpretation of the Boltzmann weight. Unfortunately in many theories of interest one…
In this work, we propose a new Galerkin-Petrov method for the numerical solution of the classical spatially homogeneous Boltzmann equation. This method is based on an approximation of the distribution function by associated Laguerre…
Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
In this paper, we extend previous work on scalar $\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external…
The fermion bag approach is a new method to tackle fermion sign problems in lattice field theories. Using this approach it is possible to solve a class of sign problems that seem unsolvable by traditional methods. The new solutions emerge…
We present a new approach for Monte Carlo simulations of lattice quantum spin systems which is able to eliminate the negative sign problem. Its complexity is linear in the volume of the lattice. Its efficiency is tested on a simple…
The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic…
In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…