hy si cs / 0 30 80 27 v 3 1 0 Se p 20 03 What is spin ?

This is a late answer to question #79 by R.I. Khrapko, “Does plane wave not carry a spin?,” Am. J. Phys. 69, 405 (2001), and a complement (on gauge invariance, massive spin 1 and 1 2 , and massless spin 2 fields) to the paper by H.C. Ohanian, What is spin?, Am. J. Phys. 54, 500–505 (1985). In particular, it is confirmed that “spin” is a classical quantity which can be calculated for any field using its definition, namely that it is just the non-local part of the conserved angular momentum. This leads to explicit expressions which are bilinear in the fields and which agree with their standard “quantum” counterparts. The problem of defining and calculating the intrinsic “spin” carried by plane waves is a recurring question (see, e.g., [1, 2]) even though it has been definitely clarified sixty years ago by J. Humblet who recognized that such a definition is only possible for a wave-packet, that is a superposition of plane waves confined to a bounded four-dimensional region of space-time [3, p.596]. This concept is in agreement with standard text books which make clear that plane waves of infinite extent are just mathematical idealizations and that physical waves correspond to “fields produced a finite time in the past (and so localized to a finite region of space)” [4, p.333], [5, p.99]. More generally, this concept agrees with Julian Schwinger’s fundamental idea of source theory, namely that “a physical description refers only to the finite space-time region which is under the experimenter’s control” [6, p.78]. Finally, in practical calculations, this concept leads to a simple recipe, applicable in many cases, which consists of approximating a wave-packet by a plane wave provided it is assumed that all contributions coming from infinitely remote space-time points (i.e., from so-called “surface terms”) are zero. It is therefore not surprising that the paper of H.C. Ohanian [1], as well as both answers to R.I. Khrapko’s question [2], i.e., [7, 8], are essentially based on this concept. These papers focus on the spin 1 electromagnetic field: What about spin 1 2 electrons, massive spin 1 particles, and possibly higher spin fields such