Galilean Symmetry of Non-Relativistic Quantum Mechanics

  • D. Giulini
Chapter

Abstract

Let G denote the (inhomogeneous) Galilei group. A general element gG is parameterized by a rotation-matrix R, a boost-velocity v and a space-time translation vector (a, b). The multiplication law is given by
$$g'g = \left( {R',v',a',b'} \right)\left( {R,v,a,b} \right) = \left( {R'R,v' + R'v,a' + R'a + v'b,b' + b} \right)$$
(A6.1)
$${g^{ - 1}} = {\left( {R,v,a,b} \right)^{ - 1}}\left( {{R^{ - 1}}, - {R^{ - 1}}v, - {R^{ - 1}}\left( {a - vb} \right), - b} \right).$$
(A6.2)
We shall throughout ignore problems that might arise due to the non-simply-connectedness of the rotation group SO(3), since we can always consider its simply-connected double cover SU(2) instead.

Keywords

Tral Disal 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

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  • D. Giulini

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