Publication

Quantum scale invariance on the lattice

Mikhail Chapochnikov, Igor Tkachev
2009
Journal Articles

Abstract

We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field - the dilaton. We describe how to select non-perturbatively the phenomenologically viable theories where the scale invariance is broken spontaneously. Relation to gravity is also discussed. (C) 2009 Elsevier B.V. All rights reserved.

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https://infoscience.epfl.ch/entities/publication/6163d31b-e873-4c7d-ac4c-d18907059fd4

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Mikhail Chapochnikov, Igor Tkachev
2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6163d31b-e873-4c7d-ac4c-d18907059fd4

About this result

Related concepts (32)

Scale invariance

In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. In mathematics, scale invariance usually refers to an invariance of individual functions or curves.

Lattice field theory

In physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a space or spacetime that has been discretised onto a lattice. Although most lattice field theories are not exactly solvable, they are of tremendous appeal because they can be studied by simulation on a computer, often using Markov chain Monte Carlo methods. One hopes that, by performing simulations on larger and larger lattices, while making the lattice spacing smaller and smaller, one will be able to recover the behavior of the continuum theory as the continuum limit is approached.

Lattice QCD

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies.

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