Particle Physics and Representation Theory
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High Quality Content by WIKIPEDIA articles! In physics, the connection between particle physics and representation theory is a natural connection, first noted by Eugene Wigner, between the properties of elementary particles and the representation theory of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, algebras corresponding to "approxim...
High Quality Content by WIKIPEDIA articles! In physics, the connection between particle physics and representation theory is a natural connection, first noted by Eugene Wigner, between the properties of elementary particles and the representation theory of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, algebras corresponding to "approximate symmetries" of the universe. In quantum mechanics, any particular particle (with a given momentum distribution, location distribution, spin state, etc.) is treated as a vector, (or "ket") in a Hilbert space. Let G be the symmetry group of the universe -- that is, the set of symmetries under which the laws of physics are invariant.
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