Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 8th 2012

    From Erhard Sholtz’s Weyl entering the ’new’ quantum mechanics discourse

    Already earlier in the 1920s,Weyl had found two topics in modern physics, in which group representations became important. The first topic was in general relativity and differential geometry. The representation theory of the special linear group SL nS L_n \mathbb{R}, showed that there is a mathematical reason for the structural importance of tensors in differential geometry.

    Footnote: All irreducible representations of SL 2S L_2 \mathbb{R}, arise as subrepresentations of tensor products of the natural representation with certain symmetry properties. Thus infinitesimal structures of classical differential geometry have a good chance to be expressible in terms of vector and tensor fields.

    Perhaps that ’2’ should be nn, but is something like this commonly understood?

    It seems very similar to the wish to find irreducible representation of powers of the natural representation of the symmetic group to yield logical operations, as reported at the Café here (cached since out of action). Mautner used tensor notation for the logical operations.