Representations of the Lorentz Group

Peter Woit ()
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Peter Woit: Columbia University, Department of Mathematics

Chapter Chapter 41 in Quantum Theory, Groups and Representations, 2017, pp 515-525 from Springer

Abstract: Abstract Having seen the importance in quantum mechanics of understanding the representations of the rotation group SO(3) and its double cover $$Spin(3)=SU(2)$$ , one would like to also understand the representations of the Lorentz group SO(3, 1) and its double cover $$Spin(3,1)=SL(2,\mathbf C)$$ . One difference from the SO(3) case is that all non-trivial finite dimensional irreducible representations of the Lorentz group are non-unitary (there are infinite dimensional unitary irreducible representations, of no known physical significance, which we will not discuss).

Keywords: Lorentz Group; Infinite-dimensional Irreducible Unitary Representations; Clifford Algebra; Quantum Field Theory Textbooks; Weyl Spinor (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-64612-1_41

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DOI: 10.1007/978-3-319-64612-1_41

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