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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Fourvectors and Operators

Fourvectors and Operators

(p.364) 17 Fourvectors and Operators
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Davis Johns

Oxford University Press

This chapter develops techniques that allow relativistically covariant calculations to be done in an elegant manner, and introduces fourvectors. These are analogous to the familiar vectors in three-dimensional Cartesian space – which will now be referred to as threevectors. The difference is that, in addition to the three spatial components, fourvectors will have an additional zeroth component associated with time which allows one to deal with the fact that the Lorentz transformation of special relativity transforms time as well as spatial coordinates. The theory of fourvectors and operators is presented using an invariant notation. Rather than considering a fourvector to be a set of components in some basis, it is considered to be something that models some physical property of the experiment under study and is independent of the choice of coordinate system.

Keywords:   relativistically covariant calculations, fourvectors, Cartesian space, threevectors, zeroth component

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