Abstract
Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. Aμ = \(A_{\mu }^{{{\text{phys}}}}\) + \(A_{\mu }^{{{\text{pure}}}}\). In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided by the contour gauge condition.
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Notes
The comprehensive analysis of the non-Abelian Stocks theorem can be found in [18].
In the local gauge, the corresponding exponential disappears thanks to the nullified integrand A+ = 0.
REFERENCES
X. Ji, F. Yuan, and Y. Zhao, Nat. Rev. Phys. 3, 27 (2021).
R. L. Jaffe and A. Manohar, Nucl. Phys. B 337, 509 (1990).
X. D. Ji, Phys. Rev. Lett. 78, 610 (1997).
X. S. Chen et al., Phys. Rev. Lett. 100, 232002 (2008).
X. S. Chen et al., Phys. Rev. Lett. 103, 062001 (2009).
X. Ji, Phys. Rev. Lett. 106, 259101 (2011).
M. Wakamatsu, Int. J. Mod. Phys. A 29, 1430012 (2014).
M. Wakamatsu, Eur. Phys. J. A 51, 52 (2015).
M. Wakamatsu et al., Ann. Phys. 392, 287 (2018).
C. Lorce, Phys. Lett. B 719, 185 (2013).
C. Lorcé, Phys. Rev. D 88, 044037 (2013).
E. Leader and C. Lorcé, Phys. Rept. 541, 163 (2014).
M. Wakamatsu, Phys. Rev. D 84, 037501 (2011).
M. Wakamatsu, Phys. Rev. D 83, 014012 (2011).
M. Wakamatsu, Phys. Rev. D 81, 114010 (2010).
P. M. Zhang and D. G. Pak, Eur. Phys. J. A 48, 91 (2012).
S. Bashinsky and R. L. Jaffe, Nucl. Phys. B 536, 303 (1998).
Y. A. Simonov, Sov. J. Nucl. Phys. 50, 134 (1989).
A. V. Belitsky and A. V. Radyushkin, Phys. Rep. 418, 1 (2005).
S. V. Ivanov et al., Sov. J. Nucl. Phys. 44, 145 (1986).
S. V. Ivanov and G. P. Korchemsky, Phys. Lett. B 154, 197 (1985).
I. V. Anikin, arXiv: 2105.09430 [hep-ph].
I. V. Anikin et al., Nucl. Phys. B 828, 1 (2010).
I. V. Anikin et al., Phys. Rev. D 95, 034032 (2017).
S. Mandelstam, Ann. Phys. 19, 1 (1962).
B. S. DeWitt, Phys. Rev. 125, 2189 (1962).
C. Lorce, Phys. Rev. D 87, 034031 (2013).
L. D. Faddeev and A. A. Slavnov, Front. Phys. 50, 1 (1980).
L. D. Faddeev and V. N. Popov, Sov. Phys. Usp. 16, 777 (1973).
H. Weigert and U. W. Heinz, Z. Phys. C 56, 145 (1992).
M. B. Mensky, Theor. Math. Phys. 173, 1668 (2012).
I. V. Anikin and O. V. Teryaev, Phys. Lett. B 690, 519 (2010).
I. V. Anikin and O. V. Teryaev, Eur. Phys. J. C 75, 184 (2015).
L. Durand and E. Mendel, Phys. Lett. B 85, 241 (1979).
Y. Hatta, Phys. Rev. D 84, 041701 (2011).
A. V. Belitsky et al., Nucl. Phys. B 656, 165 (2003).
M. Burkardt, Phys. Rev. D 88, 014014 (2013).
ACKNOWLEDGMENTS
We thank C. Lorce, D.G. Pak, M.V. Polyakov, L. Szymanowski for useful discussions. IVA is grateful to O.V. Teryaev for fruitful comments on the early stage of the work.
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Anikin, I.V., Zhevlakov, A.S. On the Decomposition Theorem for Gluons. J. Exp. Theor. Phys. 135, 73–80 (2022). https://doi.org/10.1134/S1063776122070081
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DOI: https://doi.org/10.1134/S1063776122070081