Do Leptons Have the Property of Colour?

[kurious]

Think of a proton being orbited by a single electron.Gluons in the
proton have energy and so must curve space-time and so affect the
passage of electric force-mediating photons - traveling from the
proton to the electron - through it.So the electric force and colour
force interact.This means that the electric charge of a lepton must
respond to the colour force indirectly and very weakly.
An electron and positron would be expected to have a "pure" electric
force interaction with one another.However if gluons exist in the
quantum vacuum between them,then these gluons can curve space-time and
affect the passage of force-mediating photons, and so the leptons
would be experiencing indirectly the effects of the colour force.But
is this the same as saying that the leptons have the property of
colour?

 

[mathman]

Curving of space-time is a gravity thing, not of the strong force. At the atomic level, it is immeasurably small. The color force (strong force) and the electric force don't interact.

 

[kurious]

They have to interact because any energy source like a gluon curves space-time and will affect the passage of a photon.The effect may be slight but it will be real.
A gluon getting very close to a photon could change the path of the photon considerably.

 

[marlon]

I think mathman is totally right. You cannot implement concepts of general relativity in QFT. So it is fundamentally wrong to talk about curvature of spacetime in a theory (here QFT) where Heisenbergs uncertainty-principle is valid.

And this QCD-vacuum you are talking about consists of quarkcondensates, a bit like Cooperpairs.

 

[Haelfix]

"A gluon getting very close to a photon could change the path of the photon considerably"

Doubtful, the scattering in such a situation due to gravity will be nearly infinitesally small, and completely swamped out by other things going on in the vacuum.

You can however implement qft in curved spacetime, but the drawback is its very hard to talk about 'particles' and their 'paths'.

 

[marlon]

QFT+gravity = strings ?

If we want to implement gravity in QFT we need to introduce the concept of strings and stuff, isn't it ?

Offcourse once we start talking about strings we can no longer talk about fotons and their paths because the "foton" as we know it is represented by an open string living on a brane (and only there). Gravitons which are then represented by closed strings can live anywhere. This means on a brane like our spacetime-manifold, but also on the six extra compactified dimensions in each space-time-"point". Now we are talking in terms of the 11-dimensional supergravity, right?

This gives also an explanation for the fact that these extra six dimensions cannot be seen, because fotons (light) cannot travel through these six dimensions which do not live on the brane...


Gravity can then be incorporated because gravitons live in all 11-dimensions. The only way to see the compactified dimensions would be through interactions of particles on the brane and gravitons. But the gravitational interaction is so weak that corrections due to "brane"-particles like fotons are very difficult to detect.

I think this is the way to look at things, but I could be forgetting some ingredients ?

marlon

 

[Haelfix]

Naa you don't have to introduce String theory yet. Gravity is nonrenormalizable, but you can treat it as an effective theory and look for quantum corrections, say to one loop.

People do that, and well what you end up with is field theory in curved spacetime. There are a number of subtle problems with the picture, like the difficulty in finding conserved quantities outside the boundary at infinity. there's also subtle problems with the measurement principle.

You really need to use the algebraic formalism of canonical gravity, but its doable.

It just isn't the whole story, for more you need a full fledged nonperturbative theory of quantum gravity. See String theory or something else for that.

 

[humanino]

This is ambitious I think ! I really don't know much about field theory in curved spacetime, but I think there is the Rindler effect, which says that an accelerating particle in "empty" vacuum feels itself in a thermal bath.

So Marlon, which one should be FIRST taken into account, i.e. at a given scale, which effect is the most important ? Thermal bath, curvature of spacetime, or both (is it one and the same thing ?)

 

[humanino]

Let me add that the Rindler effect is very much linked to another hot current topic : Hawking radiation and the information loss in black holes. This is happening in another forum !

 

[marlon]

Let me add that the Rindler effect is very much linked to another hot current topic : Hawking radiation and the information loss in black holes. This is happening in another forum !

hi humanino, i see we are from the same month and year...

could you explain to me a bit more on this Rindler effect, because it is new to me. Never heard of it. What exactly is its connection to the hawking radiation ?

 

[marlon]

This is ambitious I think ! I really don't know much about field theory in curved spacetime, but I think there is the Rindler effect, which says that an accelerating particle in "empty" vacuum feels itself in a thermal bath.

So Marlon, which one should be FIRST taken into account, i.e. at a given scale, which effect is the most important ? Thermal bath, curvature of spacetime, or both (is it one and the same thing ?)

When you probe at distancescales of 10^-35 meters, then gravitaional effects become important. At bigger scales, it is only the Standard Model that rules. Conterporary accelerators are able to probe at scales of about 10^-15 meters. So in our present conditions of doing exoerimental fysics, it is the nice QFT of elementary particles that will have the upperhand in explaining things...

à la prochaine fois...
marlon

 

[humanino]

I have to apologize. I was referring to the Unruh effect. Sorry ! Besides, I don't even know any such thing as Rindler effect.

The connection between the Unruh effect and the Hawking radiation must be seriously deep. As I told you, this is not my field (and this is not the right forum), but I picture those as only one phenomenon : the Unruh effect takes place in flat spacetime, and generalizes to the Hawking effect in curved spacetime. The Unruh effect is simply that a uniformly accelerating particle will find itself surrounded by a thermal heat bath of temperature proportional to the acceleration. This is really because the vacuum states are different for an inertial and a accelerated observer.

http://en.wikipedia.org/wiki/Unruh_effect
http://www.phys.lsu.edu/mog/mog17/node8.html
or hep-th/9510026

 

[humanino]

Is it possible to say that particle creation by black holes is similar to particle creation at another singularity of spacetime : the Big Bang ?

 

[vanesch]

So the electric force and colour
force interact.This means that the electric charge of a lepton must
respond to the colour force indirectly and very weakly.

There are of course couplings between a gluon and an electron within the standard model which are many many orders of magnitude stronger than a hypothetical gravitational effect, as higher-order Feynman diagrams:
A gluon can couple to a quark-anti quark loop which can couple to a photon and to an electron. This is first order in alpha-s (the gluon-quark vertex) and second-order in alpha_em (one vertex photon-quark and one vertex photon-electron).
Given that alpha-s is not very small, this is almost of the same order as photon-photon coupling.

cheers,
Patrick.