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This classical solution of the Euclidean equations of motion is often named "kink solution" and is an example of an instanton. In this example, the two "vacua" (i.e. ground states) of the double-well potential, turn into hills in the Euclideanized version of the problem.
Periodic instantons were discovered with the explicit solution of Euclidean-time field equations for double-well potentials and the cosine potential with non-vanishing energy [1] and are explicitly expressible in terms of Jacobian elliptic functions (the generalization of trigonometrical functions). Periodic instantons describe the oscillations ...
The stability of the instanton configuration in the path integral theory of a scalar field theory with symmetric double-well self-interaction is investigated using the equation of small oscillations about the instanton. One finds that this equation is a Pöschl-Teller equation (i.e. a second order differential equation like the Schrödinger ...
In theoretical physics, the BPST instanton is the instanton with winding number 1 found by Alexander Belavin, Alexander Polyakov, Albert Schwarz and Yu. S. Tyupkin. [1] It is a classical solution to the equations of motion of SU(2) Yang–Mills theory in Euclidean space-time (i.e. after Wick rotation), meaning it describes a transition between two different topological vacua of the theory.
Given B 1, B 2, I, J such that = =, an anti-self-dual instanton in a SU gauge theory with instanton number k can be constructed, All anti-self-dual instantons can be obtained in this way and are in one-to-one correspondence with solutions up to a U( k ) rotation which acts on each B in the adjoint representation and on I and J via the ...
One important example of an instanton is the BPST instanton, discovered in 1975 by Alexander Belavin, Alexander Markovich Polyakov, Albert Schwartz and Yu S. Tyupkin. [1] This is a topologically stable solution to the four-dimensional SU(2) Yang–Mills field equations in Euclidean spacetime (i.e. after Wick rotation).
The BPST instanton is a classical instanton solution to the Yang–Mills equations on ℝ 4. Yang–Mills theories are special examples of gauge theories with a non-abelian symmetry group given by the Lagrangian
Instantons have properties similar to particles, specific examples include: Calorons, finite temperature generalization of instantons. Merons, a field configuration which is a non-self-dual solution of the Yang–Mills field equation. The instanton is believed to be composed of two merons.