Abstract
By the general Poincaré group we mean the set ρ of all transformations x → x’ of Minkowski space M that leaves the interval between any pair of points of M invariant, that is, transformations such that (s’ − y’)2 = (x − y)2 for all x,y ∈ M. Each transformation of ρ automatically turns out to be an inhomogeneous linear (that is, affine) transformation; more precisely, it has the form
where a is a fixed vector of M and Λ is a transformation of the general Lorentz group. Hence it is clear that the general Poincaré group can also be defined as the set of pairs (a, Λ), where a ∈ M, Λ ∈ L, with the multiplication law
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© 1990 Kluwer Academic Publishers
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Bogolubov, N.N., Logunov, A.A., Oksak, A.I., Todorov, I.T., Gould, G.G. (1990). Relativistic Invariance in Quantum Theory. In: Bogolubov, N.N., Logunov, A.A., Oksak, A.I., Todorov, I.T. (eds) General Principles of Quantum Field Theory. Mathematical Physics and Applied Mathematics, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0491-0_7
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DOI: https://doi.org/10.1007/978-94-009-0491-0_7
Publisher Name: Springer, Dordrecht
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