ENCYCLOPEDIA 4U .com

# Encyclopedia Home Page

 Web Encyclopedia4u.com

# Instanton

In mathematical physics, the concept of instanton is more complicated in Minkowski space: in this article, we will focus on instantons in 4D Euclidean space.

If we insist that the solutions to the Yang-Mills equations have finite energy, then the curvature of the solution at infinity (taken as a limit) has to be zero. This means that the Chern-Simons invariant can be defined at the 3-space boundary.

This is equivalent, via Stoke's theorem, to taking the integral

.
This is a homotopy invariant and it tells us which homotopy class the instanton belongs to. The Yang-Mills energy is given by where * is the Hodge dual.

Since the integral of a nonnegative integrand is always nonnegative, for all real θ. So, this means If this bound is saturated, then the solution is a BPS state. For such states, either *F=F or *F=-F depending on the sign of the homotopy invariant.

Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.

Copyright © 2005 Par Web Solutions All Rights reserved.
| Privacy

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Instanton".