- #1
scariari
- 18
- 0
Im learning about quantum tunneling and read something about that there are classical solutions at imaginary times, so called instantons? Can anyone help me out with this connection?
Classical Tunneling: Instantons Explained
In summary, the conversation discusses the concept of instantons, which are classical solutions in quantum tunneling that are calculated in Euclidean spacetime and can change the winding number of the vacuum. The term "imaginary times" refers to the fact that these solutions are calculated in 4-dimensional space instead of Minkowski space. The concept of solitons, which interpolate between different vacua, is also mentioned. The reason for calling this a tunnel effect is due to the energy barrier between the two vacua states.
- #2
humanino
- 2,527
- 8
This is not easy, and maybe should be delayed until you have actually gone beyond QM, and learned a good deal of QFT.
When they say "imaginary times" it refers to the fact that those solutions are calculated in Euclidean spacetime : this is just ordinary metric 4-dim space. This is NOT Minkowski space, which is the usual way to think about vacuum (at least in classical terms).
Do you know what a soliton is ?
A soliton typically interpolates between different vacua at infinity.
http://www.maths.surrey.ac.uk/research/Geom/sg.gif
they can go through each other.
Now imagine there is only one of those around : at infinity on the left, there is not the same winding number than at infinity on the right.
An instanton is just a soliton in 4-dim space.
Actually, instantons change the winding number of the vacuum too. It is just less easy to picture in the case.
The reason we call this a tunnel effect, is that there is an energy barrier between the two vacua states.
When they say "imaginary times" it refers to the fact that those solutions are calculated in Euclidean spacetime : this is just ordinary metric 4-dim space. This is NOT Minkowski space, which is the usual way to think about vacuum (at least in classical terms).
Do you know what a soliton is ?
A soliton typically interpolates between different vacua at infinity.
http://www.maths.surrey.ac.uk/research/Geom/sg.gif
they can go through each other.
Now imagine there is only one of those around : at infinity on the left, there is not the same winding number than at infinity on the right.
An instanton is just a soliton in 4-dim space.
Actually, instantons change the winding number of the vacuum too. It is just less easy to picture in the case.
The reason we call this a tunnel effect, is that there is an energy barrier between the two vacua states.
- #3
humanino
- 2,527
- 8
and by the way : the avatar I am using is the formula which gives the winding number of the F field 
- #4
jasonc65
- 20
- 0
You mean where ds^2 = dx^2 + dy^2 + dz^2 + dt^2?humanino said:
Related to Classical Tunneling: Instantons Explained
1. What is classical tunneling?
Classical tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even though it does not have enough energy to do so classically.
2. What are instantons?
Instantons are a type of classical solution to the equations of motion in quantum field theory. They describe the tunneling of particles through potential barriers.
3. How do instantons explain classical tunneling?
Instantons explain classical tunneling by providing a mathematical description of the process. They show that particles can tunnel through barriers by following a non-classical path in spacetime.
4. What is the importance of understanding classical tunneling and instantons?
Understanding classical tunneling and instantons is important in understanding the behavior of particles at the quantum level. It has applications in various fields such as quantum computing, cosmology, and particle physics.
5. Are there any real-life examples of classical tunneling and instantons?
Yes, there are several examples of classical tunneling and instantons in real-life, such as alpha decay in radioactive materials, tunneling of electrons in a scanning tunneling microscope, and the decay of a false vacuum in the early universe.
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