Linear Algebra and Group Theory for Physicists pp 407-566 | Cite as

# The Lorentz Group and its Representations

Chapter

## Abstract

One knows from the Special Theory of Relativity that space-time transformations between two inertial frames having uniform relative motion are called Lorentz transformations. If, for example, two inertial systems *K*(*x*, *y*, *z*) and *K*′(*x*′, *y*′, *z*′) with respective time measures *t* and *t*′ are coincident at *t* = *t*′ = 0 and *K*′ moves with a uniform velocity (0, 0, *v*) along the common *z* − *z*′ axis with respect to *K* such that the *x* − *x*′ and *y* − *y*′ axes are respectively parallel.

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## References

- 1.
**I.M. Gelfand, R.A. Minlos**and**Z.Ya. Shapiro**,*Representations of the Rotation and Lorentz Groups and their Applications*, New York, Pergamon Press, 1963.Google Scholar - 2.
**I.M. Gelfand, M.I. Graev**and**N.Ya. Vilenkin**,*Generalised Functions*, vol 5, New York, Academic Press. 1966.Google Scholar - 3.
**M.A. Naimark**,*Linear Representations of the Lorentz Group*, New York, Pergamon Press, 1964.zbMATHGoogle Scholar - 4.
**E.P. Wigner**,*Unitary Representations of the Inhomogeneous Lorentz Group*, Ann. Math,**40**, 149 (1939)ADSMathSciNetCrossRefzbMATHGoogle Scholar

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