the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple...

Generalizations of Pauli matrices Representation theory of SU(2) For a characterization of U(n) and hence SU(n) in terms of preservation of the standard...

theory of the noncompact group SL(2, R) is equivalent to the representation theory of SU(2), its compact form, essentially because their Lie algebras have...

of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the...

Unitary representation Weight (representation theory) Peter–Weyl theorem Borel–Weil theorem Kirillov character formula Representation theory of SU(2) Representation...

specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...

half-integers instead. See Representation theory of SU(2). SO ( 3 ) {\displaystyle {\text{SO}}(3)} : The group of rotations of 3D space. Irreps are the...

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of...

complex conjugate of ρ ( g ) {\displaystyle \rho (g)} . In the representation theory of SU(2), the dual of each irreducible representation does turn out to...

the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was...

In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism...

Representation theory of connected compact groups Lie algebra representation Projective representation Representation theory of SU(2) Representation theory...

of SU(1,1): this was not the whole of SL(2,C), but instead a complex semigroup defined by a natural geometric condition. The representation theory of...

finite-dimensional representation theory of the universal covering group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb...

{\displaystyle m} . The general theory then tells us that for each m {\displaystyle m} , there is a unique irreducible representation of SU(2) with highest weight...

In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a...

non-compact simple real Lie group of dimension 3 with applications in geometry, topology, representation theory, and physics. SL(2, R) acts on the complex upper...

Unified Theory might actually be realized in nature. The two smallest irreducible representations of SU(5) are 5 (the defining representation) and 10...

well as respective transformations of the spin (see representation theory of SU(2)). Aircraft principal axes Change of basis Charts on SO(3) Rotations and...

Rarita–Schwinger equation Representation theory of SU(2) Spin angular momentum of light Spin engineering Spin-flip Spin isomers of hydrogen Spin–orbit interaction...

{\displaystyle H_{1}} and H 2 {\displaystyle H_{2}} are integers.) This is to be compared to the representation theory of SU(2), where the irreducible representations...

vertex. The representation theory of SU(2) goes back to the nineteenth century and the theory of invariants of binary forms, with the figures of Alfred Clebsch...

The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations...

example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing of elements of algebraic...

physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups...

field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices...

In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple...

gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge...

In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group...

U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of the understanding of the Standard...