相关论文: The aliasing problem in lattice field theory
This is a survey article describing the various ways in which the Kauffman bracket skein module is a quantization of surface group characters. These include a purely heuristic sense of deformation of a presentation, a Poisson quantization,…
Effective field theories provide a formalism for categorizing low-energy effects of a high-energy fundamental theory in terms of the low-energy degrees of freedom. This process has been well established in mapping the fundamental theory of…
Discrete Lagrangian multiform theory is a variational perspective on lattice equations that are integrable in the sense of multidimensional consistency. The Lagrangian multiforms for the equations of the ABS classification formed the start…
The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice…
Theoretical particle physicists continue to push the envelope in both high performance computing and in managing and analyzing large data sets. For example, the goals of sub-percent accuracy in predictions of quantum chromodynamics (QCD)…
We treat a relativistically moving particle interacting with a quantum field from an open system viewpoint of quantum field theory by the method of influence functionals or closed-time-path coarse-grained effective actions. The particle…
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction…
We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates…
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised…
The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near…
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
We consider the quantum Lobachevsky space ${\bf L}_q^3$, which is defined as subalgebra of the Hopf algebra ${\cal A}_q(SL_2({\bf C}))$. The Iwasawa decomposition of ${\cal A}_q(SL_2({\bf C}))$ introduced by Podles and Woronowicz allows to…
This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…
Inspired by the quantum McKay correspondence, we consider the classical $ADE$ Lie theory as a quantum theory over $\mathfrak{sl}_2$. We introduce anti-symmetric characters for representations of quantum groups and investigate the Fourier…
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles…
We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to…
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…