2021/10/03 by Yaakov Friedman · 1 citation
Physics and Astronomy · Computer Science · #Quantum and electron transport phenomena #Quantum Mechanics and Applications #Quantum Information and Cryptography
paper · pdf · doi:10.3390/sym13101853
openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
We introduced a new model to present the states of a two-state quantum system. The space is the complexified Minkowski space. The Lorentz group acts by the linear extension of its action on the four-vectors. We applied this model to represent the spin state of an electron or any relativistic spin 1/2 particle. The spin state of such particle is of the form U+iS, where U is the four-velocity of the particle in the lab frame, and S is the 4D spin in this frame. Under this description, the transition probability between two pure spin states ϱ1 and ϱ2 of particles moving with the same velocity are defined by use of Minkowski dot product as 12<ϱ2|ϱ1>. This transition probability is Lorentz invariant, coincide with the quantum mechanics prediction and thus agree with the experimental results testing quantum mechanics predictions based on Bell’s inequality. For a a particle of mass m and charge q with the spin state ϱ, the total momentum is mcϱ and the electromagnetic momentum is qϱ. This imply that the Landé g factor for such particles must be g=2. We obtain an evolution equation of the spin state in an electromagnetic field which defines correctly the anomalous Zeeman effect and the fine structure splitting.