Potential Energy of Quantum Field?

Fluxes are the names given to particular fields, typically the derivative of some particular field. For instance, \(H_{3} = dB_{2}\) and \(F_{n} = dC_{n}\), ignoring any particulars about non-standard equations of motion.

Reiku, why would a discussion on the divergence of field configurations on a compact space have anything to do with 'passages'?

 

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As I mentioned: I don't really think this has anything to do with the question I'm asking AlphaNumeric! I know the meaning of the word flux, but I don't know precisely what AlphaNumeric is referring to in relation to the rest of the differential geometry contained in his post.

 

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I wasn't even sure myself what context it was being used in.

 

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There's something called 'flux potential', for sure; that's a common expression in papers about Hall liquids - the Aharonov-Bohm effect, a few other exotic fields of electronic endeavour.

 

As you might have gathered by AN's post #61, the fluxes he is talking about ARE different from electromagnetic flux, but not THAT different.

 

So are the equations that determine the fluxes dynamical, or are they geometrical? If either of you have a spare mo to give a brief explanation, it would be trendy.

However, if it's all a bit complicated don't worry about it!!

 

Given a 10d string model, there are various consistency equations you need to consider which, in terms of QFT, reduce to the same constraints as in QED where photons have polarisations in particular dimensions (in other words, no ghosts). This means that there's 8 string oscillations in the 10 dimensions in each direction.

8*8 = 64 (Reiku, if you don't follow, just say) and the 64 modes break down as :

\(\mathbf{8} \times \mathbf{8} = G_{(ab)} + B_{[ab]} + \Phi\) where \(G_{aa} = 0\)

So the string's natural oscillations account for the traceless metric, an antisymmetric field and a string scalar which is equivalent to the string's coupling strength (\(g_{s} \equiv e^{-\Phi}\)).

The 3-form flux H is defined as dB, so in simple models you have B(x) = B, so H = 0. Otherwise you have a flux H.

Then you have that in particular view point, strings on a space-time topology which is (to some level of approximation) \(\mathcal{M}_{s} = \mathcal{M}^{4} \times \mathcal{K} \) where \(\mathcal{K}\) is some compactified space which is a quotient space whose original manifold is the product of circles (say a torus). That way you have a well defined notion of T duality. See Wiki for an explaination of T duality I'm to apathetic to give you.

Under T duality your fluxes change and via a process my PhD is based upon you end up with other fluxes. These all play a part in your equations of motion for the space-time fields but you need to know the components first.

Additional to these contributions (which as known as NS-NS fields) you have R-R contributions which as your \(F_{n}\), fields whose sources are \(C_{n-1}\) (ie \(d(C_{n-1}) = F_{n}\)), you might be familiar with in terms of electromagnetism. These also have particular expressions but are much easier to deal with than the other fluxes. They all contribute to your fields and play roles in the equations of motion.

 

So what happens in the quantum field to turn potential energy into real energy?

 

Potential energy is real energy. A brick on a table has actual potential energy.

 

Are you saying that the potential energy in a quantum field is the same as matter, i.e. real energy? If so, how does the quantum field create matter?

 

I'm probably going to have to familiarize myself a little more with the string theory side of things before I can take much from your post! Much appreciated though.

What is "energy" and how does one tell whether it is real or not?

 

Define 'real'. Because you aren't using it in any sense that physicists do.

 

Sorry. I'll make it simpler. How does a quantum field create matter?

 

It's not 'simpler', dumb ass. I am 208% certain that what I consider 'simple physics' is a trillion light years beyond what you could ever understand. The fact you ignore all the details I've given about the nature of fields in string theory demonstrates that. The details I've posted are pretty much step one in the 3rd lecture in a 24 lecture course on an introduction to string theory given to people before they even start their PhD. So please don't patronise myself or anyone else by pretending you'll dumb down your questions for us 'simple people'.

Jackass!

Now define 'matter'. Do you consider a weak boson 'matter'? It's not a particle like an electron or proton but a particle like a photon, yet it has mass. A photon doesn't have mass and some people don't consider it 'matter' but a force particle.

Energy is part of the quantification of the perturbation of a field from it's empty state. ALL fields, be they 'matter' or 'force', have they massive or massless particles, possess energy. Would you like me to walk you, VERY slowly through the process of computing this for something insultingly easy to someone like Ben, Guest or myself, like a scalar quantum field or is that 'simple' enough for you?

 

I wasn't patronizing you. I was simply eliminating the term "real", so this thread wouldn't get sidetracked on a useless discussion over semantics.
If all matter will eventually decay into photons, then I don't care about matter at this point. How about explaining how a quantum field can create photons?

 

John J. Bannan: is your philosophy to continue to ask questions until you receive an answer you understand? Whilst gutsy, it's likely to be very ineffective. What you should aim to do is understand small "blocks" of physics, bit by bit. As you get a few blocks under your belt, you can start building on them. Eventually you'll find yourself in a position to ask questions from which you can gather meaningful information. At the moment, you seem to be asking question upon question upon question, but not managing to gain any understanding.

Worth a try, perhaps?

 

I am after the most basic information physicists have to offer. I want to know the limits of their knowledge on the most basic level. If AN can't explain how a quantum field produces photons - then that's the information I'm after. However, AN persists in thinking he knows something I don't believe he does. That's why he refuses to answer my most basic questions. I don't expect an answer from AN. I expect an admission that he doesn't know.

 

I have commented on your style of questioning before, in the discussion Calabi Yaus. You continue to ask questions in a "Ha, as if you understand this. I've got your number!" attitude, as if you're trying to trap those of us who have spent more time doing physics than you've spent eating food.

Perhaps if you stopped asking a barrage of tedious questions and spent a small fraction of that time reading and thinking (I know it probably gives you a headache but it gets easier with time) about what you read and what people tell you then maybe you'd understand more?

It's not sematics, it's you using incorrect terminology.

Fields couple to one another. Hence, something like an electron can emit or absorb a photon (nb only 'charged particles' can emit or absorb photons). It does so by transferring some of it's energy and momentum into the electromagnetic quantum field.

No doubt you'll now ask "But how does it do that", hoping for some kind of simple physical analogy for your ignorant brain to wrap itself around. Unfortunately, Chuckles, not all of physics can be explained in metaphors and examples a half dead doped up 6 year old would understand. And if that's the case you're really in trouble!

/cue a stupid question...

Like what? I answer plenty of your questions. Your inability to understand doesn't mean I don't.

Let's see... it's only in about every book written on quantum field theory since Dirac developed it in about 1931. My, my, it's clearly a conspiracy of physicists to keep the information from ignorant ****s who don't bother to do any research or learn any physics. Wow, we really are keeping the truth from you, aren't we?

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And I was right about the 'attempting to back us into a corner' comment. You know NOTHING about theoretical physics, your multitude of threads recently have demonstrated that across the board and yet you think you know what I do or don't know?! WTF?

If any one of us wasn't in a particularly good mood (which I'm racing towards at the moment) we could give you a completely ontopic and relevent reply which you could have no chance of understanding.

For instance, you asked what a Calabi Yau manifold was in another thread. It's a complex manifold with a closed Kahler form possessed SU(n) holonomy. It's torsionless and has no 3-form fluxes within it (for reasons already discussed in this thread via Guest's questions). The Calabi-Yaus in string theory are when n=3 because then you're working over a 6 dimensional manifold, as needed to prevent gravitational anomalies in string theory. If you don't make the simplification of the 3-forms being zero you generalise to a space of SU(3) structure, which doesn't possess SU(3) holonomy but SU(3) structure and whose Kahler form is not closed, nor does it possess complex structure, it's an 'almost complex manifold' whose complex form and holomorphic 3-form (though such a thing doesn't even have a wel.l defined meaning in a non-complex manifold) are not closed and whose lack of closure are parameterised by 5 torsion classes.

Want me to go on or do you think you know what I do or don't know about this subject, jackass?

 

Well in that case, I think I can save you lots of trouble! Seek and ye shall find.

You want to know about the limits of current theory without knowing anything about current theory? Good luck with that one!

Forgive me if I've got this wrong, but I get the impression from your posts that you're not all that bothered in learning about physics, but you're desperately keen to ask a question that will in some way be poignant. Your strategy seems to be to ask as many questions as possible, and hopefully one of them will turn out to be a bit of a corker. You seem to want the very helpful people on this board say "we don't know enough physics for your ever so intelligent question". Even if this is your strategy, I believe you could still do well by my advice. There are lots of questions out there, most of them stupid - learning a little physics would dramatically increase the probability of you asking something profound.

 

I should also add: if you want to ask your questions simply to hear someone answer "I don't know", ask me! No doubt, I shall be able to give you an honest response that satisfies your need.