Corollary to Noether's theorem about the conservation of angular momentum and spin in theories that are dealing with strong laser fields

Abstract

We have shown that Noether's theorem [16] has a corollary which proves non-conservation of angular momentum and spin in "mixed" theories (the ones that combine classical and quantum approach). As laser field is treated classically and atoms with which it interacts must be treated as quantum objects (see, for instance [1], where the ADKtheory is described, which we take as a represent of "mixed" theories), it is shown that in such theories the law of conservation of the 4-angular momentum tensor is broken. As there are many other theories that can be defined as "mixed" [see, for instance, 18], we think the result being interesting enough, though that evident shortcoming does not affect the results of ADK-theory, because it never operates with spin, and the most probable ejected electrons have orbital quantum number l = 0 [8,17]. However it should be stressed that the corollary we have proved does not imply that the law of conservation of angular momentum and spin is not valid in general, but only that one should be cautious when treating angular momentum and spin in "mixed" theories.

Stern-Gerlach Experiment’s Interpretations and Noether’s Theorem

“…We are offering a possible explanation why! It has been stressed more than once that theories describing behavior of atoms in strong laser fields treat an atom as quantized object and electromagnetic field classically [5]. We already suggested that these theories should be called "mixed".…”