Difference between QED & QCD Vacuum

In summary, in QED vacuum there are no electrons, while in QCD vacuum there are no quarks. The difference is, QED vacuum contains no electrons, while QCD vacuum contains no quarks. There are several differences. The first one is that in low-energy QCD there is a phase with broken chiral symmetry indicated by order parameter (the so-called quark condensate) with non-vanishing expectation value. If you do that for QED (for s = electrons, positrons and photons) you find zero (as expected). But for QCD the two definitions do not coincide! So one has a vacuum state with lowest energy 0, but for which the expectation value of N does not vanish.
  • #1
dev70
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Hi pf, i have been wondering what differentiates QED Vacuum from QCD Vacuum? How would u explain its implications? I mean, how can u define pure vacuum in 2 ways?
 
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  • #2
no reply..what does that imply...:p
 
  • #3
dev70 said:
Hi pf, i have been wondering what differentiates QED Vacuum from QCD Vacuum?
The difference is, QED vacuum contains no electrons, while QCD vacuum contains no quarks. :smile:
 
  • #4
There are several differences. The first one is that in low-energy QCD there is a phase with broken chiral symmetry indicated by order parameter (the so-called quark condensate) with non-vanishing expectation value

##\langle \bar{q} q \rangle > 0##

whereas in QED the electron-positron expectation value vanishes

##\langle \bar{\psi} \psi \rangle = 0##
 
  • #5
ok..fine..then would you please explain the QED vacuum and the creation of virtual particles and more about vacuum fluctuations?
 
  • #6
What is your background in physics and your knowledge in quantum field theory?
 
  • #7
well.nothing much..just 12th grade..nd beginner of quantum physics...
 
  • #8
OK.

In quantum field theory one introduces a so-called vacuum state |vac>. This is not trivial mathematically, but the main idea is that
- the vacuum state is the state with lowest energy
- the vacuum state is empty, so the are no particles present

1) Now one can calculate the energy expectation value (in a finite volume) and one can calculate the expectation value for the particle numbers (particles species s, e.g. electrons and positrons, photons, quarks, gluons). One expectes something like

##\langle H \rangle_\text{vac} = \langle\text{vac} | H | \text{vac}\rangle = 0##
##\langle N_s \rangle_\text{vac} = \langle\text{vac} | N_s | \text{vac}\rangle = 0##

where H and N are so-called operators which define energy and particle number.

If you do that for QED (for s = electrons, positrons and photons) you find zero (as expected).

But for QCD the two definitions do not coincide!

So one has a vacuum state with lowest energy 0, but for which the expectation value of N does not vanish. So the two equations become

##\langle H \rangle_\text{vac} = \langle\text{vac} | H | \text{vac}\rangle = 0##
##\langle N_s \rangle_\text{vac} = \langle\text{vac} | N_s | \text{vac}\rangle \neq 0##

The so-called quark condensate which I introduced in the previous post is something that measure the quark content of the vacuum. So the non-vanishing of this condensate means that the vacuum (defined as the state with lowest energy) is not empty.

2) There is a related phenomenon, namely the excitatons of the vacuum. In quantum field theory these quantized excitatons are interpreted as particles.

In QED one can find states with arbitrary small energy ε>0 (ε can be any positive number). This is rather simple b/c the energy of a photon is just E=hf, so a single photon with small frequency f (long wave length λ) defines such a state

##\langle f| H | f \rangle = hf##

Again in QCD the situation is different. There is no such state with arbitrary small but non-zero energy ε. Adding a single excitatation (a quark, a gluon) results in an unphysical state which is forbidden due to symmetry reasons and due to (infinite) energy. So in QCD there is a mass-gap, which means that one must add a rather large energy (a few hundred MeV) to find the next state above the vacuum state.

3) In order not t confuse you too much I due not (yet) discuss exceptions to 2) which are closely related to 1)
 
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  • #9
this is awesome..though i won't get all of it now...but still, i will. thanks a lot...its wonderful..
 
  • #10
tom.stoer said:
##\langle N_s \rangle_\text{vac} = \langle\text{vac} | N_s | \text{vac}\rangle \neq 0##
Ok then, if it is not zero, what is its value?
 
  • #11
Bill_K said:
Ok then, if it is not zero, what is its value?
I was cheating a little bit b/c one does not determine <N> but the (flavor-specific) quark condensate; afaik the (ren.-scheme dep.) values are in the range of 300 MeV3; afaik in two-flavor QCD the value can be related to the pion mass and decay constant via the Gell-Mann–Oakes–Renner relation, e.g. in current algebra and chiral perturbation theory; there should be lattice gauge calculations as well.

I have to find some references.
 
Last edited:

1. What is QED vacuum and QCD vacuum?

QED (Quantum Electrodynamics) vacuum refers to the vacuum state in which the electromagnetic field has no particles or fluctuations. QCD (Quantum Chromodynamics) vacuum refers to the vacuum state in which the strong nuclear force has no particles or fluctuations.

2. What is the main difference between QED vacuum and QCD vacuum?

The main difference between QED vacuum and QCD vacuum is the type of force they represent. QED vacuum is associated with the electromagnetic force, while QCD vacuum is associated with the strong nuclear force.

3. How do QED and QCD vacuums affect the behavior of particles?

QED vacuum and QCD vacuum have different effects on the behavior of particles. QED vacuum allows for the creation and annihilation of virtual particles, while QCD vacuum is responsible for the confinement of quarks and gluons within particles.

4. Can QED and QCD vacuum coexist?

Yes, QED and QCD vacuum can coexist and interact with each other. In fact, QED vacuum plays a role in the formation and stability of hadrons, which are particles that are bound by the strong nuclear force.

5. How do QED and QCD vacuum affect our understanding of the universe?

The study of QED and QCD vacuum has greatly contributed to our understanding of the fundamental forces and particles in the universe. It has also helped explain the behavior of particles and the structure of matter. Additionally, QCD vacuum plays a crucial role in the theory of the strong nuclear force, which is essential for understanding the behavior of protons and neutrons in atoms.

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