Gluon field
Quantum field theory |
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History |
In theoretical particle physics, the gluon field is a four-vector field characterizing the propagation of gluons in the strong interaction between quarks. It plays the same role in quantum chromodynamics as the electromagnetic four-potential in quantum electrodynamics – the gluon field constructs the gluon field strength tensor.
Throughout this article, Latin indices take values 1, 2, ..., 8 for the eight gluon color charges, while Greek indices take values 0 for timelike components and 1, 2, 3 for spacelike components of four-dimensional vectors and tensors in spacetime. Throughout all equations, the summation convention is used on all color and tensor indices, unless explicitly stated otherwise.
Introduction
Gluons can have eight
The gluon fields for each color charge each have a "timelike" component analogous to the electric potential, and three "spacelike" components analogous to the magnetic vector potential. Using similar symbols:[1]
where n = 1, 2, ... 8 are not
The
the components of the gluon field are represented by 3 × 3 matrices, given by:
or collecting these into a vector of four 3 × 3 matrices:
the gluon field is:
Gauge covariant derivative in QCD
Below the definitions (and most of the notation) follow K. Yagi, T. Hatsuda, Y. Miake[2] and Greiner, Schäfer.[3]
The gauge covariant derivative Dμ is required to transform quark fields in manifest covariance; the partial derivatives that form the four-gradient ∂μ alone are not enough. The components which act on the color triplet quark fields are given by:
wherein i is the imaginary unit, and
is the dimensionless coupling constant for QCD, and is the strong coupling constant. Different authors choose different signs. The partial derivative term includes a 3 × 3 identity matrix, conventionally not written for simplicity.
The
The quark field ψ belongs to the
Gauge transformations
The
where
is a 3 × 3 matrix constructed from the tn matrices above and θn = θn(r, t) are eight
leaving the electromagnetic tensor F invariant.
The quark fields are invariant under the
See also
- Quark confinement
- Gell-Mann matrices
- Field (physics)
- Einstein tensor
- Symmetry in quantum mechanics
- Wilson loop
- Wess–Zumino gauge
References
Notes
- ISBN 978-0-470-03294-7.
- ISBN 0-521-561-086.
- ^ ISBN 3-540-57103-5.
Further reading
Books
- W. N. Cottingham; D. A. Greenwood (2007). An Introduction to the Standard Model of Particle Physics. Cambridge University Press. ISBN 978-113-946-221-1.
- H. Fritzsch (1982). Quarks: the stuff of matter. Allen lane. ISBN 0-7139-15331.
- S. Sarkar; H. Satz; B. Sinha (2009). The Physics of the Quark-Gluon Plasma: Introductory Lectures. Springer. ISBN 978-3642022852.
- J. Thanh Van Tran, ed. (1987). Hadrons, Quarks and Gluons: Proceedings of the Hadronic Session of the Twenty-Second Rencontre de Moriond, Les Arcs-Savoie-France. Atlantica Séguier Frontières. ISBN 2863320483.
- R. Alkofer; H. Reinhart (1995). Chiral Quark Dynamics. Springer. ISBN 3540601376.
- K. Chung (2008). Hadronic Production of ψ(2S) Cross Section and Polarization. ISBN 978-0549597742.
- J. Collins (2011). Foundations of Perturbative QCD. Cambridge University Press. ISBN 978-0521855334.
- W.N.A. Cottingham; D.A.A. Greenwood (1998). Standard Model of Particle Physics. Cambridge University Press. ISBN 0521588324.
Selected papers
- J.P. Maa; Q. Wang; G.P. Zhang (2012). "QCD evolutions of twist-3 chirality-odd operators". Physics Letters B. 718 (4–5): 1358–1363. S2CID 118575585.
- M. D’Elia, A. Di Giacomo, E. Meggiolaro (1997). "Field strength correlators in full QCD". Physics Letters B. 408 (1–4): 315–319. S2CID 119533874.)
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: CS1 maint: multiple names: authors list (link - A. Di Giacomo; M. D’elia; H. Panagopoulos; E. Meggiolaro (1998). "Gauge Invariant Field Strength Correlators In QCD". arXiv:hep-lat/9808056.
- M. Neubert (1993). "A Virial Theorem for the Kinetic Energy of a Heavy Quark inside Hadrons". Physics Letters B. 322 (4): 419–424. .
- M. Neubert; S2CID 1824834.
- V. Dzhunushaliev (2011). "Gluon field distribution between three infinitely spaced quarks". ].
External links
- K. Ellis (2005). "QCD" (PDF). Fermilab. Archived from the original (PDF) on September 26, 2006.
- "Chapter 2: The QCD Lagrangian" (PDF). Technische Universität München. Retrieved 2013-10-17.