# Questions tagged [instantons]

An instanton (pseudoparticle) is a classical solution to the equations of motion, usually of Yang-Mills theory, with a finite, non-zero action, on a Euclidean spacetime. Instantons normally dominate the path integral of Y-M theory and determine its quantum tunneling behavior. May use for merons and other topological field-theoretic configurations.

178 questions
Filter by
Sorted by
Tagged with
38 views

### What is the correct domain of integration for the index of instantons? - $\mathbb{R}^4$ or $S^4$?

I posted the original question on Math SE but it seems like a more appropriate question for Physics SE: https://math.stackexchange.com/q/4417225/ In calculating the instanton solutions for $SU(2)$ ...
• 1,091
23 views

### How to deal with actions with interfering extrema?

How can one deal with actions with multiple extrema which difference is comparable to $\hbar$ (the extrema of the action are not widely separated) in the path integral method?
• 621
1 vote
56 views

### Can a kink in a finite one dimensional box tunnel into a trivial solution?

Given a simple kink solution of the Sine Gordon equation, is it possible for such a solution in a finite volume to tunnel into a trivial vacuum solution, given that such tunneling demands a finite ...
• 621
17 views

### What if the minimising path for the least action isn't unique? [duplicate]

Using the Lagrangian method, we find the path which minimises the action. But what if multiple paths each have the same minimum action? How do we resolve such a situation?
• 4,620
129 views

• 4,630
43 views

### Gelfand-Yaglom method and perturbation

I'm reading Instantons and large $N$ (https://laces.web.cern.ch/LACES10/notes/instlargen.pdf) by Marino, and I don't understand something about Gelfand–Yaglom method (from page 22), so please tell me ...
• 83
33 views

### Can an instanton be a Wilson loop?

I was wondering if one could write an $\mathrm{SU}(N)$-instanton as a Wilson loop. Since in temporal gauge, I can interpret a YM-instanton on $M\times\mathbb{R}$ as a one-parameter family of gauge ...
• 141
84 views

### The theta term and triviality of principal bundles

Apologies if this question is trivial or has been answered before. If we consider a Yang-Mills theory (with a simple, compact Lie group $G$) on $\mathbb{R}^4$, it is well-known that all the finite-...
• 63
1 vote
136 views

• 632
102 views

### How "hedgehog" or instanton event changes the configuration of neel vector in 2D antiferromagnet?

The definition of "hedgehog" or instanton event here is "a space-time event where the skyrmion number Q changes by $\pm1$ is called a hedgehog" (ref.1 & 2). A nice figure ...
• 661
66 views

### How to visualize the $U(1)$ instanton event in (2+1)D compact lattice gauge field?

In the continuum limit of (2+1)-dimensional compact $U(1)$ gauge field, the instantons are input by hand in terms of nonconservation of magnetic flux $\int b$: \begin{eqnarray} \int dxdy [b(x,y,t+\...
• 643
74 views

127 views

### Instantons in Altland/Simons

I have a question about a statement in Condensed Matter Field Theory (2nd edition) by Altland/Simons on p.124. In short, when we consider a motion in a double well we obtain a classical solution in ...
• 321
108 views

• 2,084
102 views

### Fermionic non-zero modes to standard $SU(2)$ 't Hooft instantons?

The fermionic zero modes to the "standard" $SU(2)$ 't Hooft instantons are known as follows (see page 42 in this article): For a 't Hooft instanton (self-dual field strength tensor) in the regular ...
• 4,268