QCD Confinement: Wilson Loops & Quantum Fluctuations

In summary, the connection between the perimeter law for Wilson loops and quantum fluctuations of matter fields in the QCD Lagrangian is that the area law for appropriate Wilson loops is involved due to the quantum fluctuations of gauge (Yang-Mills, gluonic) fields. Additionally, it is questioned whether the "garmonic" potential V\sim r^2 can provide the correct infrared behaviour for confinement and the absence of (Faddeev-Popov) ghosts in the axial gauge A_3=0 is explained by ghosts not coupling to gauge fields in this gauge. Finally, the origin of the ln det G item in the Green function of the \lambda \phi^4 model is discussed.
  • #1
Leonid
6
0
Which is the connection between the perimeter law for Wilson loops and quantum fluctuations of matter fields (presenting in the QCD Lagrangian); and why quantum fluctuations of gauge (Yang-Mills, gluonic) fields infolve the area law for appropriate Wilson loops? Senk You. Leonid.
 
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  • #2
Garmonic potential

Can the "garmonic" ("squared") potential V\sim r^2 supply the correct infrared behaviour necessary for confinement (i.e. the q^(-\alpha), \alpha>0 as q\to 0 in the momentum space)?
Leonid.
 
  • #3
QCD, FP ghosts

Why (Faddeev-Popov) ghosts are absent in the axial gauge A_3=0?
Sincerelly, Leonid.
 
  • #4
because ghost does not couple to gauge field in axial gauge
 
  • #5
vertices in the path integral formalism

The origin of the ln det G item (where G(\phi) is the Green function in the \lambda \phi^4 model, for instance)?
Sincerelly, Leonid.
 

What is QCD Confinement?

QCD Confinement, or Quantum Chromodynamics Confinement, is a phenomenon in which quarks and gluons, the building blocks of protons and neutrons, are confined within particles and cannot exist as free particles.

How does QCD Confinement occur?

QCD Confinement occurs due to the strong force, which is responsible for binding quarks together. As quarks are pulled apart, the energy between them increases, making it more energetically favorable for a new quark-antiquark pair to form, rather than allowing the original quarks to exist as free particles.

What are Wilson Loops?

A Wilson Loop is a mathematical quantity used in QCD calculations to study the confinement of quarks. It represents a closed loop made up of a path in space and an associated gauge field, and is used to calculate the potential energy between quarks.

What role do quantum fluctuations play in QCD Confinement?

Quantum fluctuations, or small, random changes in the behavior of particles at the quantum level, are believed to play a crucial role in QCD Confinement. These fluctuations can lead to the creation of virtual particles, which contribute to the strong force that binds quarks together.

Why is QCD Confinement important in understanding the behavior of matter?

QCD Confinement is important in understanding the behavior of matter because it helps to explain why we only observe particles made up of quarks and not free quarks themselves. It also plays a crucial role in the formation of protons and neutrons, which make up the majority of the visible matter in the universe.

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