Search results
Results From The WOW.Com Content Network
In mathematics the spin group, denoted Spin(n), [1] [2] is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2)
Spin representations can be analysed according to the following strategy: if S is a real spin representation of Spin(p, q), then its complexification is a complex spin representation of Spin(p, q); as a representation of so(p, q), it therefore extends to a complex representation of so(n, C).
A spin model is a mathematical model used in physics primarily to explain magnetism. Spin models may either be classical or quantum mechanical in nature. Spin models have been studied in quantum field theory as examples of integrable models. Spin models are also used in quantum information theory and computability theory in theoretical computer ...
A spin network, immersed into a manifold, can be used to define a functional on the space of connections on this manifold. One computes holonomies of the connection along every link (closed path) of the graph, determines representation matrices corresponding to every link, multiplies all matrices and intertwiners together, and contracts indices in a prescribed way.
A spin C structure is analogous to a spin structure on an oriented Riemannian manifold, [9] but uses the Spin C group, which is defined instead by the exact sequence 1 → Z 2 → Spin C ( n ) → SO ( n ) × U ( 1 ) → 1. {\displaystyle 1\to \mathbb {Z} _{2}\to \operatorname {Spin} ^{\mathbf {C} }(n)\to \operatorname {SO} (n ...
Spintronics emerged from discoveries in the 1980s concerning spin-dependent electron transport phenomena in solid-state devices. This includes the observation of spin-polarized electron injection from a ferromagnetic metal to a normal metal by Johnson and Silsbee (1985) [5] and the discovery of giant magnetoresistance independently by Albert Fert et al. [6] and Peter Grünberg et al. (1988). [7]
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
The theory is one-loop finite [32] and its one-loop amplitudes are related to those of self-dual Yang-Mills theory. The theory can be thought [33] of as a higher-spin extension of self-dual Yang–Mills theory. Chiral theory admits an extension to anti-de Sitter space, where it is a unique perturbatively local higher-spin theory with ...