Gerald S. Guralnik

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Quantum field theories and Matrix models have a far richer solution set than is normally considered, due to the many boundary conditions which must be set to specify a solution of the Schwinger-Dyson equations. The complete set of solutions of these equations is obtained by generalizing the path integral to include sums over various inequivalent contours of(More)
There is a complex relationship between the architecture of a computer, the software it needs to run, and the tasks it performs. The most difficult aspect of building a brain-like computer may not be in its construction, but in its use: How can it be programmed? What can it do well? What does it do poorly? In the history of computers, software development(More)
This work develops and applies the concept of mollification in order to smooth out highly oscillatory exponentials. This idea, known for quite a while in the mathematical community (mollifiers are a means to smooth distributions), is new to numerical Quantum Field Theory. It is potentially very useful for calculating phase transitions (highly oscillatory(More)
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 known symmetries and theoretical properties of a theory. In order to test this approach, we applied it to φ theory in(More)
We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc function representation converges rapidly, and it(More)
We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin1 2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed(More)
This talk describes a program to develop a new numerical approach to the solution of quantum field theories [1] which we call the Source Galerkin method. The ideas involved have little directly in common with the Monte Carlo techniques that have demonstrated the power of numerical approaches to obtain results from quantum field theories. Source Galerkin has(More)