The dx1⊗σ3 coefficient of a BPST instanton on the (x1,x2)-slice of R4 where σ3 is the third Pauli matrix (top left). The dx2⊗σ3 coefficient (top right). These coefficients determine the restriction of the BPST instanton A with g=2,ρ=1,z=0 to this slice. The corresponding field strength centered around z=0 (bottom left). A visual representation of the field strength of a BPST instanton with center z on the compactification S4 of R4 (bottom right). The BPST instanton is a classical instanton solution to the Yang–Mills equations on R4.
An instanton (or pseudoparticle[1][2][3]) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime.[4]
In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because:
they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and
they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory.
Relevant to dynamics, families of instantons permit that instantons, i.e. different critical points of the equation of motion, be related to one another. In physics instantons are particularly important because the condensation of instantons (and noise-induced anti-instantons) is believed to be the explanation of the noise-induced chaotic phase known as self-organized criticality.
^Instantons in Gauge Theories. Edited by Mikhail A. Shifman. World Scientific, 1994.
^Interactions Between Charged Particles in a Magnetic Field. By Hrachya Nersisyan, Christian Toepffer, Günter Zwicknagel. Springer, Apr 19, 2007. Pg 23
^Large-Order Behaviour of Perturbation Theory. Edited by J.C. Le Guillou, J. Zinn-Justin. Elsevier, Dec 2, 2012. Pg. 170.
^Vaĭnshteĭn, A. I.; Zakharov, Valentin I.; Novikov, Viktor A.; Shifman, Mikhail A. (1982-04-30). "ABC of instantons". Soviet Physics Uspekhi. 25 (4): 195. doi:10.1070/PU1982v025n04ABEH004533. ISSN 0038-5670.
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion...
In mathematical physics and differential geometry, a gravitational instanton is a four-dimensional complete Riemannian manifold satisfying the vacuum...
In theoretical physics, the BPST instanton is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu...
Periodic instantons are finite energy solutions of Euclidean-time field equations which communicate (in the sense of quantum tunneling) between two turning...
In quantum field theory, the instanton fluid model is a model of Wick rotated Euclidean quantum chromodynamics. If we examine the path integral of the...
BPST-like instantons. Although only the solutions with one or few instantons (or anti-instantons) are known exactly, a dilute gas of instantons and anti-instantons...
a symplectic manifold with the symplectic action functional. For the (instanton) version for three-manifolds, it is the space of SU(2)-connections on...
With Stephen Hawking, he later developed the so-called Hawking-Turok instanton solutions which, according to the no-boundary proposal of Hawking and...
topology of smooth 4-manifolds using moduli spaces of anti-self-dual instantons. It was started by Simon Donaldson (1983) who proved Donaldson's theorem...
his more recent work was inspired by theoretical physics, in particular instantons and monopoles, which are responsible for some corrections in quantum field...
algebra Kac–Moody algebra Wess–Zumino–Witten model Gauge theory Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie...
the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld,...
either tunnel through the barrier (in which case the transition is an instanton-like process) or must for a reasonable period of time be brought up to...
a non-trivial homotopy group, or, in physics lingo, in terms of instantons. Instantons are a form of topological soliton; they are a solution to the classical...
of non-tunneling rates. Instantons, a field configuration which is a local minimum of the Yang–Mills field equation. Instantons are used in nonperturbative...
Gerard 't Hooft. Polyakov and coauthors discovered the so-called BPST instanton which, in turn, led to the discovery of the vacuum angle in QCD. His path...
University. He has conducted research in gauge theory, string theory, instantons, black holes, strong interactions, and many other topics. He was awarded...
caloron is the finite temperature generalization of an instanton. At zero temperature, instantons are the name given to solutions of the classical equations...
north and south pole Dyon, a particle with electric and magnetic charge Instanton, a class of field solutions that includes monopoles Monomial, a polynomial...
forms through a process known as bubble nucleation. In this process, instanton effects cause a bubble containing the true vacuum to appear. The walls...
algebra Kac–Moody algebra Wess–Zumino–Witten model Gauge theory Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie...