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The local picture of electron spin is studied in the framework of quantum electrodynamics(QED).
In the framework of QED, one of the fundamental local physical quantities is the energy-momentum tensor density, which is derived from the general principle of relativity.
Recently, the “quantum spin vorticity theory”[1] is proposed as a consequence of the general relativistic symmetry of the energy-momentum tensor.
The quantum spin vorticity theory can give the time evolution equations of the electronic momentum density and the spin angular momentum density as equations which relate local mechanical physical quantities derived from the energy-momentum tensor density.
These local images of an electronic state by the quantum spin vorticity theory can help us to understand spin phenomena in condensed matter and molecular systems from a unified viewpoint [2,3].

[1] A. Tachibana, J. Math. Chem. 50, 669 (2012); Electronic Stress with Spin Vorticity. In Concepts and Methods in Modern Theoretical Chemistry, S. K. Ghosh and P. K. Chattaraj. Eds., CRC Press, Florida (2013), pp. 235-251; J. Comput. Chem. Jpn. 13, 18 (2014); Indian J. Chem. A, 53, 1031 (2014).
[2] M. Fukuda, K. Soga, M. Senami, A. Tachibana, Int. J. Quant. Chem., 116, 920 (2016)
[3] M. Fukuda, K. Ichikawa, M.Senami, A. Tachibana, AIP Advances 6, 025108 (2016).

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