I don't have my books handy at the moment, but it's elementary. I imagine Peskin & Schroder or any introduction on QFT covers this.

Im holding Lewis Ryder in my hands right now, can we use that?

I'd like to use chapter 7, path integral quantization: gauge fields

I haven't read his book, but most likely. I would step back to where he talks about creation, annihilation, and number operators rather than jumping to path integrals though.

I was working on path integration in gauge field theory, but I will check the index for those operators

the only place in this book (according to the index) where those operators are mentioned is for the real klien gordan field

I am studying the lie group and lie algebra structure of the full lorentz group, not the real klein gordan field

I am unclear as to what you are talking about, just that its not QED or QCD or any specific QFT

I have Weinberg volume I, is your reference in this book?

On page 62, in the section "One Particle States", Weinberg covers classical topics in the Poincare group. But there is like, a lot more going on in this section than just one particle states, imho

We have a disagreement

I mean, I understand you disagree with me, but we have to agree to disagree or find a reference

I can quote plenty of things to back up the claim there is no such physical concept as a quantum field with a finite number of particles, but I feel like I already did that in multiple other ways

You've found a chapter in a book right in front of you called "one particle states." I'm not sure what more reference I can give you.

*sigh

If you put an electron in a box, how many electrons are in the box?

I said this chapter does not say you what you said

you have not given me a reference

I am trying to find something to verify what you said

not what is in a book I have read 4 times

You said "I'm not sure what more reference I can give you." How about more than zero refeerences?

Chris, how should I put one electron in a box?

should I hold it in my hand and place it in there?

'there is no such physical concept as put one electron in a bo

x

btw, a "one particle state" refers to a wave function, which you have to square to get a probability, not a number of physical objects you are countin

It's non-trivial to isolate single particles to be sure, but it has been done. Are you aware of optical tweezers?

tbh, not really

i just wiki'd it tho

thats cool! =)

Quite :)

but you can't hold a single electron still

Have you looked at cloud chambers or any other kind of particle detection? You can see the trajectories of individual particles.

and when it moves, it will generate lots of currents of virtual particles, right?

yes, I am very familiar with clouds chambers

in Landau, its stated very clearly and I previously quoted it in this chat

I will requote because I LOVE LOVE LOVE this quote a lot

its underlined in my copy which has my notes all over it from 15 years ago lol =P

"The description of such processes as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics" (Landau, Vol 4, Introduction)

this means that the path of a particle in a cloud chamber has the structure of a fractal /END

Is an optical tweezer a laser trap?

This reminds me of the bose einstein condesate

tbh, I have been out of the game for ~ 15 years and doing pure math and comp sci, but I am a physics person first and foremost

and business, fwiw, I have a lot more I could say about my personal life and things I have worked on and the research I have done, but I would prefer to focus on my current research, which was the reason I created my original question

I will await your reply

Despite the name and some PopSci coverage on the topic, "virtual particles" aren't really "particles" in the same sense. But even if you include virtual particles, you can compute an expectation value for the number of particles in a state.

Since photons are massless, there are states with IR divergences in which that number is infinite, but critically the "infinite" there vanishes if you impose any energy cutoff on the energy of a photon that is detectable.

@MattCalhoun Yes.

If you trap an atom in optical tweezers, how many atoms do you have?

nice! see I did know what optical tweezers were, I just thought they were called laser traps

Lets assume its a hydrogen atom, for a physical example

well, what are the electrons doing?

they are jumping up and down states

there is no way to "freeze time"

(I am very interested in time, did you read my blog article which is very long and covers every subject in all of theoretical physics and the role time plays?)

when an electron jumps down a state, it releases a photon

an atom exists in the universe of the non-relativistic approximation

electrons jumping around continuously in time (whatever time is(?)) exists in the universe of quantum electro dynamics

for every regime of energy, there is a physical theory which can provide a good approximation

at the length scales of a single atom, the non relativistic approximation is ifne

*fine. Thats irrelevant to me. Because I want to know more about electrons, photons, gravity, and space time.

in other words, I don't care about the non-relativistic approximation at all. I exclusively care about the length scales which are many orders of magnitude smaller than one atom. /END

Well anyway I don't have more time to spend on this today. You're free to pose this as a question on the main site. Try to keep your question short, simple, and on point.

ok, thanks

I still don't know how to phrase it properly unfortunately =( But I am sure I could phrase it poorly =)

i am not planning to post this as a question at this time

I claim that in order to measure (in the real actual world in a lab) the number of photons in an electromagnetic field a finite space (the room that is your lab), it's required to take a measurement over for a duration of infinite time. This immediately follows as a theorem (clearly, imo) from everything I have said in this chat in my formal statements until this point.

But since there is no such physical concept such as "an amount of time which is greater than a duration of infinite time", this means the number of photons in a quantum electromagnetic field is infinite /