Representation theory of the Galilean group | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Representation_theory_of_the_Galilean_group


00:00:29 diag(1, 0, 0, 0)) and the (independent) dual metric (gμν
00:08:36 0 and m  0. (The last case is similar to the first.)  In 3 + 1 dimensions, when In m  0, we can write, w
00:14:34 See also



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SUMMARY
=======
In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics)  in terms of the representation theory of the Galilean group, which is the spacetime symmetry group of nonrelativistic quantum mechanics.
In 3 + 1 dimensions, this is the subgroup of the affine group on (t, x, y, z), whose linear part leaves invariant both the metric (gμν = diag(1, 0, 0, 0)) and the (independent) dual metric (gμν = diag(0, 1, 1, 1)). A similar definition applies for n + 1 dimensions.
We are interested in projective representations of this group, which are equivalent to unitary representations of the nontrivial central extension of the universal covering group of the Galilean group by the one-dimensional Lie group R, cf. the article Galilean group for the central extension of its Lie algebra. The method of induced representations will be used to survey these.
We focus on the (centrally extended, Bargmann) Lie algebra here, because it is simpler to analyze and we can always extend the results to the full Lie group through the Frobenius theorem.

  
    
      
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