In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the Callan–Symanzik equation is a differential equation

Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

 describing the evolution of the n-point correlation functions

Correlation function (quantum field theory)

In quantum field theory, the matrix element computed by inserting a product of operators between two states, usually the vacuum states, is called a correlation function....

 under variation of the energy scale at which the theory is defined and involves the beta-function of the theory and the anomalous dimensions. This equation has the following structure


being the beta function and the scaling of the fields.

In quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

 this equation takes the form


being n and m the number of electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s and photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s respectively.

It was discovered independently by Curtis Callan

Curtis Callan

Curtis Callan is a theoretical physicist and a professor at Princeton University. He has conducted research in gauge theory, string theory, instantons, black holes, strong interactions, and many other topics...

 and Kurt Symanzik

Kurt Symanzik

Kurt Symanzik was a German physicist working in quantum field theory.- Life :Symanzik was born in Lyck , East Prussia, and spent his childhood in Königsberg. He started studying physics in 1946 at Universität München but after a short time moved to Werner Heisenberg at Göttingen...

 in 1970. Later it was used to understand asymptotic freedom

Asymptotic freedom

In physics, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become arbitrarily weak at energy scales that become arbitrarily large, or, equivalently, at length scales that become arbitrarily small .Asymptotic freedom is a feature of quantum...

.

This equation arises in the framework of renormalization group

Renormalization group

In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...

. It is possible to treat the equation using perturbation theory

Perturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

.

Literature

• Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena , Oxford University Press
  Oxford University Press
  Oxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
  
   2003, ISBN 0-19-850923-5
• John Clements Collins, Renormalization, Cambridge University Press
  Cambridge University Press
  Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
  
  1986, ISBN 0-521-31177-2