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Applied Computational Physics$
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Joseph F. Boudreau and Eric. S. Swanson

Print publication date: 2017

Print ISBN-13: 9780198708636

Published to Oxford Scholarship Online: February 2018

DOI: 10.1093/oso/9780198708636.001.0001

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Rotations and Lorentz transformations

Rotations and Lorentz transformations

Chapter:
(p.455) 14 Rotations and Lorentz transformations
Source:
Applied Computational Physics
Author(s):

Joseph F. Boudreau

Eric S. Swanson

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198708636.003.0014

A computational approach to rotations and Lorentz transformation is presented. The discussion starts with the mathematical properties of the rotation and the proper orthochronous Lorentz groups. Rotation and Lorentz transformations are implemented by exponentiating generators of SU(2). This approach allows rotations of states in a finite-dimensional Hilbert space to be carried out with the same machinery used to rotate ordinary vectors and it allows Lorentz boosts of Dirac spinors to be carried out with the same machinery used to boost four-vectors. Rotations and boosts can be applied to other objects with simple transformation properties. A computational approach to the helicity formalism used in scattering and decay theory is presented, and a library devoted to the manipulation of objects in spacetime is introduced.

Keywords:   rotation, Lorentz transformation, vector, four-vector, spinor, Dirac spinor, spacetime, Hilbert space, exponentiation, helicity formalism, spacetime

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