A tutorial on conformal groups

Ian Porteous

ArticleOriginal scientific text

Title

A tutorial on conformal groups

Authors ¹

Affiliations

Department of Pure Mathematics, The University of Liverpool, PO Box 147, Liverpool L69 3BX, U.K.

Abstract

Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to

ℝ^{p, q}

, the real vector space

ℝ^{p + q}

, furnished with the quadratic form

x^{(2)} = x \cdot x = - x_{1}^{2} - x_{2}^{2} - ... - x_{p}^{2} + x_{p + 1}^{2} + ... + x_{p + q}^{2}

, and especially with a description of this group that involves Clifford algebras.

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Title

A tutorial on conformal groups

Affiliations

Abstract

Bibliography