geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
Given a tensor product of two representations of some Lie group (by default often the special orthogonal group ) and given its decomposition into a direct sum of irreducible representations by an isomorphism
then the matrix elements of this linear map in some standard basis are called – in the physics literature – the Clebsch-Gordan coefficients or equivalently (up to a constant) the Wigner 3j symbols .
Specifically for the rotation group in 3-dimensional Cartesian space, then the standard basis elements of the representation of total angular momentum are traditionally denoted
and their inner product is traditionally denoted by
In these basis elements that above matrix then has components given by
These expressions are specifically the Clebsch-Gordan coefficients as they appear in the physics literature.
Lecture notes include for instance
Last revised on January 6, 2017 at 11:24:05. See the history of this page for a list of all contributions to it.