Abstract
Different operators of quark and gluon momenta, orbital angular momenta, and gluon spin have been used in nucleon structure studies. Their precise meaning is reviewed with respect to gauge invariance, Lorentz covariance and canonical quantization rules. The advantage and disadvantage of different definitions are analyzed. We concentrate on our gauge invariant decomposition of the total momentum and angular momentum into quark and gluon parts based on the separation of the gauge potential into a gauge invariant (covariant) physical part and a gauge dependent pure gauge part. The Lorentz covariance and measurability of our operators are demonstrated.
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Jaffe R.L., Manohar A.: The g 1 problem: deep inelastic electron scattering and the spin of proton. Nucl. Phys. B 337, 509–546 (1990)
Zeng J.Y.: Quantum Mechanics. Academy, Beijing (2000)
Gottfried K.: Quantum Mechanics, pp. 103–116. Benjamin, New York (1966)
Ji X.: Comment on Spin and OAM in gauge theories. Phys. Rev. Lett. 104, 039101 (2010)
Ji X.: Comment on Spin and OAM in gauge theories. Phys. Rev. Lett. 106, 259101 (2010)
Dirac P.A.M.: Gauge-invariant formulation of quantum electrodynamics. Can. J. Phys. 33, 650–660 (1955)
Feynman R.P., Leighton R.B., Sands M.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley, Reading, MA (1963)
Chen X.S., Wang F.: The Problem of gauge invariance in the current study of nucleon spin. Commun. Theor. Phys. 27, 121–124 (1997)
Ji X.: Gauge-invariant decomposition of nucleon spin. Phys. Rev. Lett. 78, 610–613 (1997)
Chen, X.S., Wang, F.: Gauge invaiance and hadron structure (1998). arXiv:hep-ph/9802346 [hep-ph]
Chen X.S., Lü X.F., Sun W.M., Wang F., Goldman T.: Spin and OAM in gauge theories: nucleon spin structure and multipole radiation revisited. Phys. Rev. Lett. 100, 232002-1–232002-4 (2008)
Chen, X.S., Lü, X.F., Sun, W.M., Wang, F., Goldman, T.: Spin and OAM in gauge theories: nucleon spin structure and multipole radiation revisited: Do gluons carry half of the nucleon momentum? Phys. Rev. Lett. 103, 062001-1–062001-4 (2008)
Bliokh, K.Y., Dressel, J., Nori, F.: Conservation of the spin and OAMs in electromagneytism. New J. Phys. 16, 093037 (2014). arXiv:1404.5486 [physics.optics]
Beth R.A.: Mechanical detection and measurement of the AM of light. Phys. Rev. 50, 115–125 (1936)
Allen L. et al.: OAM of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992)
Van Enk S.J., Nienhuis G.: Commutation rules and eigenvalues of spin and OAM of radiation fields. J. Modern Opt. 41, 963–977 (1994)
Bashinsky S.V., Jaffe R.L.: Quark and gluon OAM and spin in hard process. Nucl. Phys. B 536, 303–317 (1999)
Sun W.M., Chen X.S., Lü X.F., Wang F.: Gauge invariant hydrongen-atom Hamiltonian. Phys. Rev. A 82, 012107-1–012107-5 (2010)
Goldman T.: Gauge invariance time-dependent Foldy–Wouthuysen transformation, and the Pauli Hamiltonian. Phys. Rev. D 15, 1063–1067 (1977)
Kobe D.H., Yang K.H.: Gauge-invariant non-relativistic limit of an electron in a time-dependent electromagnetic field. J. Phys. A 13, 3171–3185 (1980)
Ji X.D., Xu Y., Zhao Y.: Gluon spin, canonical momentum, and gauge symmetry. JHEP 1208, 082 (2012)
Li J.F., Jiang Y., Sun W.M., Zong H.S., Wang F.: New application of decomposition of U(1) gauge potential: Aharonov–Bohm effect and Andereson–Higgs mechanism. Mod. Phys. Lett. B 26, 1250124-1–1250124-9 (2012)
Wong, C.W., Wang, F., Sun, W.M., Lü, X.F.: Gauge-invariant momentum and angular momentum operators in quantum electrodynamics and chromodynamics (2010). arXiv:1010.4336 [hep-ph]
Leader, E., Lorce, C.: The AM contraversy: What’s it all about and does it matter? (2013). arXiv:1309.4235 [hep-ph]
Bjorken J.D., Drell S.D.: Relativistic Quantum Fields. McGraw-Hill, New York (1965)
Weinberg S.: The Quantum Theory of Fields, vol. 1. Cambridge University Press, Cambridge (1996)
Zhang P.M., Pak D.G.: On gauge invariant nucleon spin decomposition. Eur. Phys. J. A 48, 91–95 (2012)
Chen X.S., Sun W.M., Wang F., Goldman T.: Proper identification of the gluon spin. Phys. Lett. B 700, 21–24 (2011)
Wakamatsu, M.: Gauge- and frame-independent decomposition of nucleon spin. Phys. Rev. D 83, 014012 (2011)
Ji X., Zhang J.H., Zhao Y.: Physics of Gluon helicity contribution to proton spin. Phys. Rev. Lett. 111, 112002 (2013)
Lorcé C., Pasquini B.: Quark wigner distributions and orbital angular momentum. Phys. Rev. D 84, 014015 (2011)
Hatta Y.: Notes on the orbital angular momentum of quarks in the nucleon. Phys. Lett. B 708, 186–190 (2012)
Hatta Y., Yoshida S.: Twist analysis of the nucleon spin in QCD. JHEP 1210, 080 (2012)
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Wang, F., Wong, C.W., Chen, X.S. et al. Gauge Invariance, Lorentz Covariance and Canonical Quantization in Nucleon Structure Studies. Few-Body Syst 56, 249–255 (2015). https://doi.org/10.1007/s00601-015-0969-9
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DOI: https://doi.org/10.1007/s00601-015-0969-9