A Virtual Fermions and Pauli Principle

[Marrrrrrr]

Hi guys,

Do virtual particles, when they are fermions, obey Pauli exclusion principle as real fermions do?
More specifically, what I am wondering is the following: Fermion fields would have some energy at every point in spacetime due to the uncertainty principle. Now, is it possible for the fields to have exactly the same energy density at two distinct spatiotemporal points? In other words, is it possible that two distinct points in a spacetime empty of matter (like de Sitter) are indistinguishible in terms of the properties of the fields at those points?

I am wondering if spatiotemporal points themselves could be viewed as quantum noise, so to speak.

Thanks.

 

[haael]

Hi guys,
Do virtual particles, when they are fermions, obey Pauli exclusion principle as real fermions do?

In most theories, yes. However, there are non-standard theories where they don't.

More specifically, what I am wondering is the following: Fermion fields would have some energy at every point in spacetime due to the uncertainty principle.

No. Fields (including fermion fields) have value at every point of spacetime. Not energy but value. Energy is an observable that acts on the field. Some fields may have energy, some may have undefined energy. Energy is a property of the field as a whole.

Now, is it possible for the fields to have exactly the same energy density at two distinct spatiotemporal points?

There is no such thing as an energy density of a field. You may only think about the energy density as a macroscopic parameter.

Speaking of values - yes, a fermion field may have the same value at two different points.

In other words, is it possible that two distinct points in a spacetime empty of matter (like de Sitter) are indistinguishible in terms of the properties of the fields at those points?

Yes, that is possible (provided you are talking about field values, not energy) and this is one of the approaches at tackling topology in QM.

I am wondering if spatiotemporal points themselves could be viewed as quantum noise, so to speak.
Thanks.

This sentence does not mean anything.

 

[Vanadium 50]

Do virtual particles, when they are fermions, obey Pauli exclusion principle as real fermions do?

Since this is an A-level thread, you should be able to answer this yourself. Write down the wavefunction of a virtual fermion and discuss its symmetry properties.