Rotations and Spinors
It is a well-known fact that rotations in three-dimensional Euclidean space can be represented by means of complex 2 × 2 matrices and that this representation is related to the stereographic projection of complex numbers (see, e.g., Goldstein 1980, Penrose and Rindler 1984, Burn 1985, Sattinger and Weaver 1986, Stillwell 1992). However, the form in which these results are usually established is somewhat indirect and, therefore, it is difficult to appreciate the naturalness of these relationships and their geometric origin (cf. Also Misner, Thorne and Wheeler 1973).
KeywordsDirac Equation Poisson Bracket Pauli Matrice Stereographic Projection Spinor Index
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