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CRC Press eBooks

Spin-1/2 Particles

Richard P. Feynman

Published Feb 19, 2018• 0 citations
Publisher

Abstract

Recall the two-component spinor, whose behavior under space rotations of angle θ about unit vector n was described by the operator exp (i θ n · M), where M = (1/2)σ. In Problem 21-3 you were concerned with the behavior of this spinor under Lorentz transformation. As was the case in space rotations it is sufficient to consider infinitesimal transformations. We write the corresponding operator as 1 + i ( v / c ) ⋅ N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429492501/e6a0c676-1f8d-4684-97a0-6bf3353f7ce0/content/eq413.tif"/>

DOI
10.1201/9780429492501-22

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Calculate the square A → ⋅ S → 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn13_1.tif"/> of the scalar product of an arbitrary vector A → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn13_2.tif"/> and of the spin vector S → = S x i → + S y j → + S Z k → . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn13_3.tif"/>