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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

Schrodinger Equation Election Rule Superselection Rule Galilei Group Universal Central Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

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  • D. Giulini

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