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The classification of the irreducible infinite-dimensional representations of the Lorentz group was established by Paul Dirac's doctoral student in theoretical physics, Harish-Chandra, later turned mathematician, [nb 3] in 1947.
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry:
Tung, Wu-Ki (1985). "Chapter 10. Representations of the Lorentz group and of the Poincare group; Wigner classification". Group Theory in Physics. World Scientific Publishing Company. ISBN 978-9971966577. Weinberg, S. (2002). "Chapter 2. Relativistic quantum mechanics". The Quantum Theory of Fields. Vol. I. Cambridge University Press. ISBN 0-521 ...
In mathematics, the representation theory of the Poincaré group is an example of the ... "Infinite irreducible representations of the Lorentz group", Proc. R ...
In mathematics, the orthogonal group in dimension n, ... The group O(3, 1) is the Lorentz group that is ... the representation theory of the orthogonal Lie algebras ...
Since the orthogonal group is a subgroup of the general linear group, representations of () can be decomposed into representations of (). The decomposition of a tensor representation is given in terms of Littlewood-Richardson coefficients c λ , μ ν {\displaystyle c_{\lambda ,\mu }^{\nu }} by the Littlewood restriction rule [ 12 ]
The rotation group SO(3) is a symmetry of Euclidean space and all fundamental laws of physics, the Lorentz group O(3,1) is a symmetry group of spacetime of special relativity. The special unitary group SU(3) is the symmetry group of quantum chromodynamics and the symplectic group Sp( m ) finds application in Hamiltonian mechanics and quantum ...
In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space.Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on the vector space.