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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 ...
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 ...
The BPST instanton is a solution to the anti-self duality equations, and therefore of the Yang–Mills equations, on R 4. This solution can be extended by Uhlenbeck 's removable singularity theorem to a topologically non-trivial ASD connection on S 4 .
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).
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.
From a physical point of view, a gravitational instanton is a non-singular solution of the vacuum Einstein equations with positive-definite, as opposed to Lorentzian, metric. There are many possible generalizations of the original conception of a gravitational instanton: for example one can allow gravitational instantons to have a nonzero ...