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An instanton can be used to calculate the transition probability for a quantum mechanical particle tunneling through a potential barrier. One example of a system with an instanton effect is a particle in a double-well potential. In contrast to a classical particle, there is non-vanishing probability that it crosses a region of potential energy ...
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 ...
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 ...
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.
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 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 ...
These equation imply the Yang–Mills equations in any dimension, and in real dimension four are closely related to the self-dual Yang–Mills equations that define instantons. In particular, when the complex dimension of the Kähler manifold X {\displaystyle X} is 2 {\displaystyle 2} , there is a splitting of the forms into self-dual and anti ...
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.