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8 - Garden of Delights
Effrosyni Seitaridou, Emory University, Atlanta, Alfred C. K. Farris, Emory University, Atlanta
Book:

A Student's Guide to Rotational Motion

Published online:

07 August 2023

Print publication:

03 August 2023, pp 157-167
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Summary

The journey through rotational motion is not quite done. In fact, we are just beginning. This chapter introduces a few topics which would be covered in an intermediate-level mechanics course. The topics include more advanced physical phenomena, such as gyroscopic precession, and the mathematical formalism of parameterizing rotations using matrices.

Appendix F - Wigner Rotation Matrices and Angular Momentum
Claudio Zannoni
Book:

Liquid Crystals and their Computer Simulations

Published online:

21 July 2022

Print publication:

28 July 2022, pp 566-573
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Summary

A concise, but fairly comprehensive summary of rotation operators, angular momentum and Wigner functions, with their combination expressions and an explicit tabulation up to order four.

12 - Statistics, Symmetry, and the Spin-Statistics Theorem
from Part I - General Properties of Fields; Scalars and Gauge Fields
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 108-117
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Summary

We define statistics of quantum mechanical particles, obtaining the Bose–Einstein and Fermi–Dirac varieties of indistinguishable particles. After finding the rotation and Lorentz matrices in different Lorentz representations, we describe the spin-statistics theorem, relating fermions with half-integer spin and bosons with integer spin. We explain two simple proofs and say some words on two others. We end by discussing symmetries in more generality, and we discuss the fact that internal symmetries must commute with spacetime ones, due to the Coleman–Mandula theorem.