Spin and space
In this paper we will take a careful look at the well-known fact that a complete 2π rotation in three dimensional space, while leaving vectors, tensors and generally the integral representations of the rotation group unchanged, causes a sign change in the half-integral spinor representations of the rotation group. First, in a brief introduction, we review the origin of the sign change of spinors by a 2π rotation. Next, we analyze Aharonov and Susskind's (hereafter referred to as A. & S.) (1967) original proposal for detecting such a sign change and compare it with a later proposal1 for detecting the sign change using neutron beams that are coherently split and recombined. While the A. & S. experiment is, we think, conceptually more interesting, the neutron beam experiment has actually been carried out. And finally, we discuss the philosophical significance of the rotationally induced spinor sign change.
KeywordsDimensional Space Integral Representation Neutron Beam Spinor Representation Rotation Group
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