Summary: Comment on ``Spin and statistics in nonrelativistic quantum mechanics: The spin-zero case''
R. E. Allen and A. R. Mondragon
Center for Theoretical Physics, Texas A&M University, College Station, Texas 77843, USA
Received 11 April 2003; published 14 October 2003
We emphasize that there is no spin-statistics connection in nonrelativistic quantum mechanics. In several
recent papers including Phys. Rev. A 67, 042102 2003 , quantum mechanics is modified so as to force a
spin-statistics connection, but the resulting theory is quite different from standard physics.
DOI: 10.1103/PhysRevA.68.046101 PACS number s : 03.65.Ta
It has been known for many years that there is a spin-
statistics connection in relativistic quantum field theory
14 but not in nonrelativistic quantum mechanics 5 .
However, several recent papers 68 have led to some con-
fusion regarding the second point.
Let us first remind ourselves why there is no spin-
statistics theorem in nonrelativistic quantum mechanics. The
essential reason is that the restrictions that imply a spin-
statistics connection in relativistic field theory are no longer
meaningful in nonrelativistic physics. For example, Wein-
berg's textbook 3 provides a relatively simple and physical
proof based on microcausality, or the requirement that com-