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

[PeterDonis]

aren't "real" particles only a mathematical tool too?

All of our models are mathematical tools. But some entities in our models correspond to things we can directly detect in reality. Others don't. "Real particles" (with appropriate qualifications for what that term means) are examples of the former. "Virtual particles" are examples of the latter.

 

[PeterDonis]

there's also an enormous lay public fascinated by physics without the mathematical training researchers have. For them, science most definitely is about stories.

Even if this is the case, it's irrelevant here at PF, because here at PF we help people to understand the actual mainstream physics, not the pop science "stories" that are told to the lay public. People who just want the pop science "stories" can go elsewhere to discuss them.

 

[PeterDonis]

if scientists are not able to convey these stories because "science is not about stories", the gap between academia and the lay public will only increase.

This is off topic for this thread.

 

[billtodd]

So, when do we use pQCD and when do we use non-pQCD (p for perturbative) in our calculations?
I can also ask the bot, but first try the humans.

If in non-pQCD we don't use the notion of virtual particles, it seems that one should opt doing the calculations in non-pQCD, but obviously it might not be practical (I haven't yet learned non-pQCD).

On another notion, I am trying to understand the mass gap problem here:
https://en.wikipedia.org/w/index.php?title=Mass_gap&section=1&oldid=1236681154&action=edit

Does a Harmonic Oscillator have this mass gap property?
I asked the famous chatGPT, but as I have been told not to post its answer I'll let you answer.

 

[A. Neumaier]

So, when do we use pQCD and when do we use non-pQCD (p for perturbative) in our calculations?

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.

Does a Harmonic Oscillator have this mass gap property?

Trivially yes.

 

[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.