Remarks on the Theory of Angular Momenta

Details Remarks on the Theory of Angular Momenta Remarks on the Theory of Angular Momenta

2003-05-09

arxiv.org/abs/quant-ph/0305049v3

Physics

Quantum Physics

4 pages; gauge invariance commented

Scientific paper

Rigorous application of the correspondence rules shows that the orbital angular momentum of a particle in an electromagnetic field is given by $\hat{L}=\vec{r}\times(-i\hbar\grad-\frac{e}{c}\vec{A}$). Thus, despite the general opinion on the corresponding rules of quantization, the eigenvalues of the angular momentum depend of the configuration of electromagnetic field. Furthermore the usual commutation rules, $[\hat{l}_i,\hat{l}_j]=i\hbar\epsilon_{ijk}\hat{l}_k$, that are at the ground of the calculus of angular momenta and of the theory of spin--and Bohm's example of the EPR argument--are not valid in presence of an electromagnetic field. Actually, the expected value of the operators $\hat{l_i}$ is not invariant under gauge transformations.

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