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2021
The purpose of this chapter is to introduce the basic idea of the lattice formalism. First, we review the quantization via the Feynman path integral. Then, we discuss the lattice regularization of both free boson systems and free fermion systems. We encounter the lattice gauge theory with the gauge principle afterwards.
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The purpose of this chapter is to introduce the basic idea of the lattice formalism. First, we review the quantization via the Feynman path integral. Then, we discuss the lattice regularization of both free boson systems and free fermion systems. We encounter the lattice gauge theory with the gauge principle afterwards.
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Approach to equilibrium in a lattice field theory
Il Nuovo Cimento B, 1982We give further results on the approach to equilibrium of a chain of coupled nonlinear oscillators when the energy is initially fed only to the longest-wave-length modes. We show that the intrinsic time scale for numerical simulations strongly depends upon the initial conditions, increasing as the coupling constant and/or the total energy are lowered ...
MARCHESONI, Fabio, M. SPARPAGLIONE
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Pramana, 1985
Lattice field theories are described as a way to regularize continuum quantum field theories. They are obtained by replacing ordinary space time by a lattice, space time derivatives by suitable differences and Minkowski by Euclidean space. The connection between a quantum field theory isd space dimension and classical statistical mechanics in (d+1 ...
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Lattice field theories are described as a way to regularize continuum quantum field theories. They are obtained by replacing ordinary space time by a lattice, space time derivatives by suitable differences and Minkowski by Euclidean space. The connection between a quantum field theory isd space dimension and classical statistical mechanics in (d+1 ...
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Langevin simulations of lattice field theories
Physical Review D, 1985We present a new analysis of Langevin simulation techniques for lattice field theories, including a general discussion of errors and algorithm speed. We introduce Fourier techniques that greatly accelerate simulations on large lattices. We also introduce a new technique for including quark vacuum-polarization corrections that admits any number of ...
, Batrouni +5 more
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Reports on Progress in Physics, 1984
The use of lattice approximations to study relativistic quantum field theories is surveyed. The models for scalar, gauge and fermionic degrees of freedom are defined. The standard methods for analytic study of these models using strong coupling, duality and mean field methods are outlined. The important area of numerical Monte Carlo simulations is also
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The use of lattice approximations to study relativistic quantum field theories is surveyed. The models for scalar, gauge and fermionic degrees of freedom are defined. The standard methods for analytic study of these models using strong coupling, duality and mean field methods are outlined. The important area of numerical Monte Carlo simulations is also
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1994
Let us remind ourselves of the basic problem in Euclidean field theory, which is to give meaning to the Schwinger functions when the action ...
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Let us remind ourselves of the basic problem in Euclidean field theory, which is to give meaning to the Schwinger functions when the action ...
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Novel Approach to Lattice Field Theory
Physical Review Letters, 1988A novel action-variational approach based on certain natural criteria is proposed. Its accuracy and advantages are demonstrated for U(1) gauge theory in four dimensions.
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Lattice field theory as a percolation process
Physical Review Letters, 1988For a given lattice spin or gauge theory an associated correlated bond or plaquette percolation process is constructed. It is conjectured to reproduce the universal scaling behavior of the original model. Different field theories lead to different cluster weights generalizing a result by Fortuin and Kasteleyn for Potts models.
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Overrelaxation algorithms for lattice field theories
Physical Review D, 1988We study overrelaxation algorithms for the thermalization of lattice field theories with multiquadratic and more general actions. Overrelaxation algorithms are one-parameter generalizations of the heat-bath algorithm which satisfy the detailed-balance condition; the parameter is the relaxation parameter ..omega.., 0 ..0 (extreme underrelaxation) limit ...
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Embedding lattice field theory in continuum field theory
Physical Review D, 1980Lattice field theory is embedded in ultraviolet-finite continuum theory by transforming a finite number of continuum degrees of freedom into lattice degrees of freedom. The resulting Hamiltonian is equivalent to the continuum Hamiltonian, and consists of the lattice Hamiltonian plus corrections.
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