Relativistic spin operator must be intrinsic

Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory

“…A related issue is the search for a right definition of relativistic spin operator, which still has no universally agreed upon definition (cf. [14,15,[43][44][45][46][47]) whereas the paper [2] assumed it as the operator 1 ⊗ 1 2 τ defined on the space Eq. (6.1a).…”

Effective descriptions of localization in a proper-time parametrized framework

“…We have recently shown [1] that the quantization of relativistic systems through a proper-time parametrized formalism is a promising framework in the quest for a solution to the so-called localization problem in relativistic quantum mechanics [2][3][4][5][6][7][8], which is also intimately connected to the issue of the adequate definition of the relativistic spin concept [9][10][11][12][13][14][15]. The proposed formalism is based on a covariant description of localization given by POVMs derived from the components of a closed but non-self-adjoint four-position operator, an approach that leads to the existence of an intrinsic temporal uncertainty for all acceptable single-particle physical states.…”

On the measurement predictions concerning the intrinsic relativistic spin operator

“…Although the concept of spin has been known for almost a century [1][2][3], its adequate relativistic definition remains a subject of intense discussion [4][5][6][7][8][9][10][11], a renewed interest on the topic having been motivated mainly by its relevance in the context of relativistic quantum information theory [12][13][14][15]. The lack of consensus concerning this definition has its roots in ambiguities regarding the properties that such a concept should satisfy [9,11,[16][17][18] and also in its direct relationship with the problem of localization, which suffers from several technical difficulties in the quantum relativistic scenario [19][20][21][22][23][24][25][26]. However, we have recently shown that the relativistic spin definitions present in literature in general fail to satisfy an essential premise concerning the spin concept: its intrinsicality [11].…”

“…The lack of consensus concerning this definition has its roots in ambiguities regarding the properties that such a concept should satisfy [9,11,[16][17][18] and also in its direct relationship with the problem of localization, which suffers from several technical difficulties in the quantum relativistic scenario [19][20][21][22][23][24][25][26]. However, we have recently shown that the relativistic spin definitions present in literature in general fail to satisfy an essential premise concerning the spin concept: its intrinsicality [11].…”

“…Qualitatively, the definition of an intrinsic property in the special relativity framework can be understood in terms of the dependence of this property with regard to the hyperplane related to which it is defined: the mathematical object that represents an intrinsic property cannot depend on the orientation of the hyperplane on which it is measured (punctual Lorentz invariance) or on the point of intersection of the observer's world line with the measurement hyperplane (space-like translational invariance). This definition led us in [11] to a unique relativistic spin operator that adequately incorporates the expected non-relativistic behavior together with the fundamental premise of intrinsicality. Adopting Minkowski's metric with signature (+, −, −, −) and Penrose's abstract index notation [27], the intrinsic spin for a system of fixed mass m is given by the tensor operator…”