Wigner's Classification
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High Quality Content by WIKIPEDIA articles! In mathematics and theoretical physics, Wigner's classification is a classification of the nonnegative energy irreducible unitary representations of the Poincaré group, which have sharp mass eigenvalues. It was proposed by Eugene Wigner, for reasons coming from physics?see the article particle physics and representation theory.The mass mequiv sqrt{P^2} is a Casimir invariant of the Poincaré group. So, we can classify the representations according to whether m 0, m = 0 but P0 0 and m = 0 and mathbf{P}=0.For the first case, we note that the eigenspace…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics and theoretical physics, Wigner's classification is a classification of the nonnegative energy irreducible unitary representations of the Poincaré group, which have sharp mass eigenvalues. It was proposed by Eugene Wigner, for reasons coming from physics?see the article particle physics and representation theory.The mass mequiv sqrt{P^2} is a Casimir invariant of the Poincaré group. So, we can classify the representations according to whether m 0, m = 0 but P0 0 and m = 0 and mathbf{P}=0.For the first case, we note that the eigenspace (see generalized eigenspaces of unbounded operators) associated with P0 = m and Pi = 0 is a representation of SO(3). In the ray interpretation, we can go over to Spin(3) instead. So, massive states are classified by an irreducible Spin(3) unitary and a positive mass, m.