Potential Energy of Quantum Field?

Oh, clever you

Good for him/her; it's called "proof"

Well, if you refuse to write it down, how can anyone know if it is any good?

what does this mean, exactly?

Publish what, exactly?

Say what - "release the math", and see what happens. From your post, I should be disinclined to trust your "gut"

What has? Scrambled eggs? Right enough there!

This makes no sense at all, as far as I can see

Please explain what a "line item unit" is. You don't, by any remote chance, mean the Riemann line element in spacetime, do you? I hope not, since otherwise yours would be a nonsensical assertion

In short, as far as I can judge, you are just one more overly egotistical idiot on this sub-forum.

How low have we stooped here.......

 

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Whilst I can't guarantee it's good, my gut tells me it's awesome. I shall be scouring the top mathematical journals in the next few months - watch this space.

 

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unless you go to a relative frame of reference, then bending space and other fun stuff somes into play but in the apple story of such, the question was asked what is the force.... and i suggest the rate is not related to any constant and the velocity.

planck's constant is wrong, even dirac ..ly stated

yes it is, as 'enquiring minds, want to know'

the best 'kind' of people

ok then what's the force? not the product. what is increasing without simply suggesting velocity

can you see the point of how this discussion is related?

that inversed square rule has a bunch to do with the increased energy noted by distance and the rate but not quite the way newton suggested, remember he was much like a darwin and defines the process but not the phenomenon that causes it.

take a read on casimir and note the exchange and increased potential, then see that rule based on the energy between the plates and distance

take a read and then ask what you will

we looking at what is the cause (force) that increase for the additional potential between bodies of mass

 

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Apologies for muddying the waters. BenTheMan and I were talking about something that shouldn't affect your questions, or the nature of the answers. Interesting it was though, nonetheless.

 

No. The potential is responsible for the force. The gradient of the gravitational potential at any given point is defined to be the force on the apple. In other words, the earth creates a potential well in which the apple sits. The steepness of the well at the specific point where the apple sits gives the force due to gravity on the apple.

Ask again and you'll get the same answer.

 

Ben is right.

 

Mod Note:

Bishadi has been banned one day for trolling.

 

Topologies which possess torsion require you to sometimes work with a modified exterior derivative. For instance, in string theory, if you turn on your 3-form H flux then you end up with a space whose derivatives work like \(d \to d_{H} = d+H \wedge\), when working on certain things. The constraints on your space remain \(d_{H}^{2} = 0\) but not only does this give you a notion of closure etc but also it gives you the constraint equations for the fluxes at the same time.

Obviously (like duh!

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) it's not going to give you a p-form because \(d : \Lambda^{(p)} \to \Lambda^{(p+1)}\) and \(H \wedge : \Lambda^{(p)} \to \Lambda^{(p+3)}\) but you are supposed to apply them to 'formal sums of p-forms', such as \(F_{RR} = F_{1}+F_{3}+F_{5}\) and \(d_{H}F_{RR}=0\). So you pluck out the various p-form equations and they will each individually be true, such as \(dF_{3} + H \wedge F_{1} = 0\). Thus your modified equation of motion is changed since \(F_{3}\) is not closed unless H=0 (ie no torsion) or \(F_{1}=0\) and so forth.

Further complications occur when you start applying T dualities and ....

[notices the blank stares]

Errr..... never mind...

Should anyone hate themselves, an example of people putting that into effect is here. Let's just say, I know a nicer way

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Well I don't think the topologies require you to work with a modified exterior derivative, do they? I mean, give me a differentiable manifold and I can plod along with my exterior derivative on the cotangent bundle and no one will mind. Talking about torsion means I've brought in extra structure (a connection). De Rham cohomology works on any smooth manifold; it's independent of a connection (and hence torsion). I think your \(\mathrm{d}_{H}\) is a type of exterior covariant derivative. This would make sense I guess, as you say it's connected with torsion.

Is it really true that \(\mathrm{d}^2_H=0\) - I can't see how it would hold on an arbitrary k-form?!?!

 

In the Yang-Mills equation you also define a covariant exterior derivative. Is this the same thing?

 

Yes - in Yang-Mill's you're working with a connection on a fibre bundle.

 

Not really, but if it can make your life easier

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For instance, in the paper I linked to that's precisely the method they use to solve the main constrain equations, they reformulate their derivatives to include these extra fields and then see how they work in the simplest examples of various p-forms and from that the solutions are a bit more forth coming.

As for \(d_{H}^{2}=0\), that arises in that system because you have MORE fluxes in the space which means that \(d_{[a_{0}}\lambda_{a_{1}a_{2}\ldots a_{n}]} = \omega_{[a_{0}a_{1}}^{b^{1}}\lambda_{b_{1}a_{2}\ldots a_{n}]}^{\phantom{b}}\) and so considering \(d_{H}^{2}=0\) leads you to something like \(\omega^{a}_{[bc}\omega_{d]a}^{e}\) and \(\omega^{a}_{[bc}H_{de]a}=0\). It's those which you're trying to solve and by expressing them as being the result of a new form of derivative on the manifold, you can approach them in a different manner than just working out specific flux entries and trying to stab at solutions.

Anyone who loves crazy weird differential geometry, like where the breakdown in the 1-1 relation between lightest modes from a Kaluza-Klein reduction and elements in \(H^{1,2}(X)\), should look up SU(3) structure. Sorta arises from questions like "When is a Calabi Yau not like a Calabi Yau and how far can it go from a Calabi Yau before we should call it something different?" :shrug: or should that be :bawl:

I'll type up a more coherent explaination tomorrow when I'm not using a tiny laptop. I have typing lots when I'm not using my own PC.

 

I don't really know much about "fluxes" and what-not I'm afraid, so sadly your post doesn't mean much to me! The point I was trying to get across is that the conversation BenTheMan and I had stands irrespective of whether or not you've got non-zero Torsion on your manifold.

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I can show you a nice piccy, of some quantised magnetic flux, if you like.

It's my avatar at the mo, I dug it up from a online Science news feed.

 

I have a feeling that's not the same kind of "flux" AlphaNumeric was referring to! But I'd like to know more, if AlphaNumeric is willing to share a little?

 

There's another kind too. It's used to help solder flow when it gets heated, and keeps all those leads on all those chips connected to various metal tracks.
I used to inhale this flux stuff, from time to time as I worshiped at the altar of my electronics hobby.
(could explain a few things...)

 

I'm still don't think that's the same type of "flux" - I was thinking of it in context to the differential geometry he was talking about.

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Flux can sometimes mean a ''passage.''

 

Yeah, sadly that's still not helping. I think I'll wait for AlphaNumeric!

 

I think he's having his morning nap, just now.

P.S. the idea of flux, is just the idea of flow. There's a liquid model for the dynamics of single-electron transfer across a Coulomb barrier.
The "flow" builds much like a drop of water at the tip of a burette does. The electron only jumps, or "drips" across the barrier, like a drop of fluid.