The Poincaré Group and its Representations

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

Chapter Chapter 42 in Quantum Theory, Groups and Representations, 2017, pp 527-539 from Springer

Abstract: Abstract In chapter 19 , we saw that the Euclidean group E(3) has infinite dimensional irreducible unitary representations on the state space of a quantum free particle. The free particle Hamiltonian plays the role of a Casimir operator: to get irreducible representations, one fixes the eigenvalue of the Hamiltonian (the energy), and then the representation is on the space of solutions to the Schrödinger equation with this energy. There is also a second Casimir operator, with integral eigenvalue the helicity, which further characterizes irreducible representations.

Date: 2017
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DOI: 10.1007/978-3-319-64612-1_42

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