Abstract
I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone’s theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2N), recovering a result originally found by Weinberg using different methods.
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Brodsky, S.J., Pauli, H.C., Pinsky, S.S.: Quantum chromodynamics and other field theories on the light cone. Phys. Rept. 301, 299-486 (1998) [hep-ph/9705477]
Belitsky, A.V., Radyushkin, A.V.: Unraveling hadron structure with generalized parton distributions. Phys. Rept. 418, 1-387 (2005) [hep-ph/0504030]
Beane, S.R.: Broken Chiral Symmetry on a Null Plane. Annals Phys. 337, 111-142 (2013) [arXiv:1302.1600 [nucl-th]]
Weinberg S.: Algebraic realizations of chiral symmetry. Phys. Rev. 177, 2604–2620 (1969)
Dirac P.A.M.: Forms of Relativistic Dynamics. Rev. Mod. Phys. 21, 392–399 (1949)
Leutwyler H., Stern J.: Relativistic Dynamics on a Null Plane. Annals Phys. 112, 94 (1978)
Jegerlehner F.: On the existence of light-like charges in quantum field theory. Helv. Phys. Acta 46, 824–843 (1974)
Kim, Y., Tsujimaru, S., Yamawaki, K.: Can the Nambu-Goldstone boson live on the light front?. Phys. Rev. Lett. 74, 4771-4774 (1995) [Erratum-ibid. 75, 2632 (1995)] [hep-ph/9502214]
Yamawaki, K.: Zero mode problem on the light front. [hep-th/9802037]
Gell-Mann M., Oakes R.J., Renner B.: Behavior of current divergences under SU(3) x SU(3). Phys. Rev. 175, 2195–2199 (1968)
Carlitz R.D., Heckathorn D., Kaur J., Tung W.K.: Chiral Symmetry and the Quark Model. Phys. Rev. D 11, 1234 (1975)
Wu, M.H., Zhang, W.M.: Chiral symmetry in light front QCD. JHEP 0404, 045 (2004) [hep-ph/0310095]
Leutwyler H., Stern J.: Covariant Quantum Mechanics on a Null Plane. Phys. Lett. B 69, 207 (1977)
Weinberg, S.: Strong interactions at low-energies. Chiral Dynamics Workshop 1994:0003-13 [hep-ph/9412326]
Witten E.: Baryons in the 1/n Expansion. Nucl. Phys. B 160, 57 (1979)
Gervais J.L., Sakita B.: Large N QCD Baryon Dynamics: Exact Results from Its Relation to the Static Strong Coupling Theory. Phys. Rev. Lett. 52, 87 (1984)
Dashen, R.F., Manohar, A.V.: Baryon - pion couplings from large N(c) QCD. Phys. Lett. B 315, 425-430 (1993) [hep-ph/9307241]
Dashen R.F., Jenkins E.E., Manohar A.V., The 1/N(c) expansion for baryons. Phys. Rev. D 49, 4713 (1994) [Erratum-ibid. D 51, 2489 (1995)] [hep-ph/9310379]
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Beane, S.R. Goldstone’s Theorem on a Light-Like Plane. Few-Body Syst 56, 523–529 (2015). https://doi.org/10.1007/s00601-015-0995-7
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DOI: https://doi.org/10.1007/s00601-015-0995-7