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In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for understanding a variety of electronic properties.
Toën, B. "Stacks and non-abelian cohomology" (PDF). Archived from the original (PDF) on January 14, 2014. Lurie, Jacob (2009). Higher Topos Theory. Annals of ...
In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at least one pair of elements a and b of G, such that a ∗ b ≠ b ∗ a. [1] [2] This class of groups contrasts with the abelian groups, where all pairs of group elements commute.
(This statement generalizes to any sheaf of groups G, not necessarily abelian, using the non-abelian cohomology set H 1 (X,G).) By definition, an E-torsor over X is a sheaf S of sets together with an action of E on X such that every point in X has an open neighborhood on which S is isomorphic to E, with E acting on itself by translation.
In the summer 1953, Yang and Mills extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to non-abelian groups, selecting the group SU(2) to provide an explanation for isospin conservation in collisions involving the strong interactions. Yang's presentation of the work at Princeton in February 1954 was ...
The quaternion group has the unusual property of being Hamiltonian: Q 8 is non-abelian, but every subgroup is normal. [4] Every Hamiltonian group contains a copy of Q 8. [5] The quaternion group Q 8 and the dihedral group D 4 are the two smallest examples of a nilpotent non-abelian group.
Merriam-Webster defines "fruit" as "the usually edible reproductive body of a seed plant." Most often, these seed plants are sweet and enjoyed as dessert (think berries and melons), but some ...
It is the first case of a Lie group that is both a compact group and a non-abelian group. The first condition implies the representation theory is discrete: representations are direct sums of a collection of basic irreducible representations (governed by the Peter–Weyl theorem). The second means that there will be irreducible representations ...