The claymath 4-d QFT problem and virtual particles (as an example)

[billtodd]

You? Your calculations? Did you ever do calculations in quantum field theory?

Both perturbative (Schwinger-Dyson based) and nonperturbative QCD (on lattices) are approximate and have their uses.

Trivially yes.

How do you show it mathematically according to the Wiki page?
I mean the definition of mass gap there is that you first need to find the two point function of the H.O..
I guess they refer to $x(t)$ of the H.O., and I see that it's indeed proportional to $\cos(\omega t)=(e^{i\omega t}+e^{-i\omega t})/2$; but in the definition of the mass gap, the $\Delta_n$ aren't imaginary numbers.

So I would still like that someone will show me how to prove that H.O indeed has a mass gap, I don't mind if it's trivial.
https://physics.stackexchange.com/q...he-ground-state-of-simple-harmonic-oscillator


P.S
does the wiki page of the mass gap refer to the wave function or other correlation functions?
I can't recall any distinctions in the classes I took in QT about correlation functions and wave functions.

BTW, the famous bot said there's no mass gap in the case of the Harmonic Oscillator, but he may make mistakes as usual...:-)

 

[A. Neumaier]

How do you show it mathematically according to the Wiki page?
I mean the definition of mass gap there is that you first need to find the two point function of the H.O..

The mass gap is the difference between the energy of the first excited state and the ground state, hence is positive whenever the spectrum is discrete.

In a quantum field theory, it can be expressed in terms of the 2-point function. But the harmonic oscillator has no 2-point function since it is not a quantum field theory.