**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Clebsch–Gordan coefficients

Summary

In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly). The name derives from the German mathematicians Alfred Clebsch and Paul Gordan, who encountered an equivalent problem in invariant theory.
From a vector calculus perspective, the CG coefficients associated with the SO(3) group can be defined simply in terms of integrals of products of spherical harmonics and their complex conjugates. The addition of spins in quantum-m

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related units

No results

Related publications (2)

Loading

Loading

Related concepts (15)

Related people

Spherical harmonics

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientifi

Angular momentum operator

In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of ato

Total angular momentum quantum number

In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentu

No results

Related courses (2)

PHYS-313: Quantum physics I

The objective of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

PHYS-431: Quantum field theory I

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

Related lectures (2)

We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O(3) singlet s, vector phi, and rank-2 symmetric tensor t. We determine their scaling dimensions to be (Delta(phi), Delta(s), Delta(t)) = (0.518942(51), 1.59489(59), 1.20954(23)), and also bound various operator product expansion coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor t(4), which we find to be relevant with Delta(t4) < 2.99056. The conformal bootstrap thus provides a numerical proof that systems described by the critical O(3) model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.

Muhammad Ahmad, Georgios Anagnostou, Konstantin Androsov, Alexandre Aubin, Roberto Castello, Yixing Chen, Tian Cheng, Giuseppe Codispoti, Alessandro Degano, Charles Dietz, Milos Dordevic, Dipanwita Dutta, Matthias Finger, Francesco Fiori, Ruchi Gupta, Csaba Hajdu, Alexis Kalogeropoulos, Viktor Khristenko, Donghyun Kim, Ji Hyun Kim, Vineet Kumar, Ajay Kumar, Sanjeev Kumar, Ekaterina Kuznetsova, Ho Ling Li, Wei Li, Hao Liu, Shuai Liu, Werner Lustermann, Matteo Marone, Thomas Muller, Ioannis Papadopoulos, Vladimir Petrov, Quentin Python, Andrea Rizzi, Paolo Ronchese, Sourav Sen, Ashish Sharma, Varun Sharma, Lesya Shchutska, Muhammad Shoaib, Michal Simon, Gurpreet Singh, Jan Steggemann, Wei Sun, Marco Trovato, Andromachi Tsirou, Paul Turner, Joao Varela, Rui Wang, Qian Wang, Zheng Wang, Jian Wang, Matthias Weber, Matthias Wolf, Meng Xiao, Zhirui Xu, Fan Yang, Yong Yang, Kai Yi, Lei Zhang

Measurements of the five most significant angular coefficients, A0 through A4 , for Z bosons produced in pp collisions at s=8 TeV and decaying to μ+μ− are presented as a function of the transverse momentum and rapidity of the Z boson. The integrated luminosity of the dataset collected with the CMS detector at the LHC corresponds to 19.7fb−1 . These measurements provide comprehensive information about the Z boson production mechanisms, and are compared to the QCD predictions at leading order, next-to-leading order, and next-to-next-to-leading order in perturbation theory.

2015