## Abstract

The static quark potential arises from vacuum fluctuations of the gauge fields; this is clear from the fact that the potential is extracted from the vacuum expectation value of a Wilson loop. In a Euclidean functional integral, the orientation of a rectangular *R* × *T* loop is obviously irrelevant to the expectation value, and in particular it can be oriented in a plane at a fixed time.

## Access this chapter

Tax calculation will be finalised at checkout

Purchases are for personal use only

## Notes

- 1.
As already mentioned in Chapter 9, it may still be useful in a physical gauge to introduce Faddeev-Popov ghosts in the path integral, but the essential point is that in a physical gauge these ghosts do not propagate in time.

- 2.
For a recent attempt to overcome this difficulty by inclusion of monopole fields, cf. [12].

- 3.
In quantum gravity this subspace of the set of all configurations is known as “minisuperspace.”

- 4.
The subtraction of λ

_{0}is introduced so that spectrum of*D*^{2}− λ_{0}+*m*^{2}begins at*m*^{2}, rather than infinity in the continuum limit. Apart from this subtraction, the proposal is the same as an earlier suggestion by Samuel [14]. - 5.
More precisely, it is the eigenstate of the lattice transfer matrix

*T*= exp[−*Ha*] with the highest eigenvalue. - 6.
Recently some corrections to σ have been calculated [19], and they are small. At present it is not entirely clear

*why*the correction is so small, since it involves a sum of rather large (positive and negative) contributing terms, which for some reason nearly cancel.

## References

Greensite, J.: Calculation of the Yang–Mills vacuum wave functional. Nucl. Phys. B

**158**, 469–496 (1979)Greensite, J.: Large scale vacuum structure and new calculational techniques in lattice SU(N) gauge theory. Nucl. Phys. B

**166**, 113–124 (1980)Halpern, M.B.: Field strength and dual variable formulations of gauge theory. Phys. Rev. D

**19**, 517–530 (1979)Greensite, J.: Computer measurement of the Yang–Mills vacuum wave functional in three-dimensions. Phys. Lett. B

**191**, 431–436 (1987)Greensite, J., Iwasaki, J.: Monte Carlo study of the Yang–Mills vacuum wave functional in D = 4 dimensions. Phys. Lett. B

**223**, 207–212 (1989)Arisue, H.: Monte Carlo measurement of the vacuum wave function for non-Abelian gauge theory in D = 3 dimensions. Phys. Lett. B

**280**, 85–90 (1992)Greensite, J., Olejnik, S., Zwanziger, D.: Coulomb energy, remnant symmetry, and the phases of non-Abelian gauge theories. Phys. Rev. D

**69**, 074506-1–074506-18 (2004)Szczepaniak, A.P., Swanson, E.S.: Coulomb gauge QCD, confinement, and the constituent representation. Phys. Rev. D

**65**, 025012-1–025012-23 (2002) [arXiv:hep-ph/0107078]Szczepaniak, A.P.: Confinement and gluon propagator in Coulomb gauge QCD. Phys. Rev. D

**69**, 074031-1–074031-14 (2004) [arXiv:hep-ph/0306030]Reinhardt, H., Feuchter, C.: On the Yang–Mills wave functional in Coulomb gauge. Phys. Rev. D

**71**, 105002-1–105002-6 (2005) [arXiv:hep-th/0408237]Feuchter, C., Reinhardt, H.: Variational solution of the Yang–Mills Schrodinger equation in Coulomb gauge. Phys. Rev. D

**70**, 105021-1–105021-21 (2004) [arXiv:hep-th/0408236]Szczepaniak, A.P., Matevosyan, H.H.: A model for QCD ground state with magnetic disorder. Phys. Rev. D

**81**, 094007-1–094007-6 (2010) [arXiv:1003.1901 [hep-ph]]Greensite, J., Olejnik, S.: Dimensional reduction and the Yang–Mills vacuum state in 2 + 1 dimensions. Phys. Rev. D

**77**, 065003-1–065003-15 (2008) [arXiv:0707.2860 [hep-lat]]Samuel, S.: On the 0++ glueball mass. Phys. Rev. D

**55**, 4189–4192 (1997) [arXiv:hep-ph/9604405]Meyer, H.B., Teper, M.J.: Glueball Regge trajectories in (2 + 1)-dimensional gauge theories. Nucl. Phys. B

**668**, 111–137 (2003) [arXiv:hep-lat/0306019]Greensite, J., Olejnik, S.: Coulomb confinement from the Yang–Mills vacuum state in 2 + 1 dimensions. Phys. Rev. D

**81**, 074504-1–074504-8 (2010) [arXiv:1002.1189]Karabali, D., Kim, C., Nair, V.P.: On the vacuum wave function and string tension of Yang–Mills theories in (2 + 1)-dimensions. Phys. Lett. B

**434**, 103–109 (1998) [arXiv:hep-th/9804132]Bringoltz, B., Teper, M.: A precise calculation of the fundamental string tension in SU(N) gauge theories in 2 + 1 dimensions. Phys. Lett. B

**645**, 383–388 (2007) [arXiv, hep-th/0611286]Karabali, D., Nair, V.P., Yelnikov, A.: The Hamiltonian approach to Yang–Mills (2 + 1): An expansion scheme and corrections to string tension. Nucl. Phys. B

**824**, 387–414 (2010) [arXiv:0906.0783 [hep-th]]Witten, E.: Global aspects of current algebra. Nucl. Phys. B

**223**, 422–432 (1983)Leigh, R.G., Minic, D., Yelnikov, A.: On the glueball spectrum of pure Yang–Mills theory in 2 + 1 dimensions. Phys. Rev. D

**76**, 065018-1–065018-23 (2007) [arXiv:hep-th/0604060]

## Author information

### Authors and Affiliations

### Corresponding author

## Rights and permissions

## Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

## About this chapter

### Cite this chapter

Greensite, J. (2010). The Vacuum Wavefunctional. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14382-3_12

### Download citation

DOI: https://doi.org/10.1007/978-3-642-14382-3_12

Published:

Publisher Name: Springer, Berlin, Heidelberg

Print ISBN: 978-3-642-14381-6

Online ISBN: 978-3-642-14382-3

eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)