What is the relativistic spin operator?

Abstract

Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic quantum mechanics. We investigate the properties of different proposals for a relativistic spin perator. It is shown that most candidates are lacking essential features of proper angular momentum operators, leading to spurious Zitterbewegung (quivering motion) or violating the angular momentum algebra. Only the Foldy-Wouthuysen operator and the Pryce operator qualify as proper relativistic spin operators. We demonstrate that ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally.

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• General relativity effects in precision spin experimental tests of fundamental symmetries
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• Spin Operator and Entanglement in Quantum Field Theory
• Dynamics of the relativistic electron spin in an electromagnetic field
• Relativistic spin operator must be intrinsic
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• One and two spin$-1/2$ particles systems under Lorentz transformations
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• Operators of quantum theory of Dirac's free field
• Spin dynamics in relativistic light-matter interaction
• Proper relativistic position operators in 1+1 and 2+1 dimensions
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