Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 object 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 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 14th 2012
   • (edited May 14th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[DHR superselection theory]]_ I have added the argument ([here](http://ncatlab.org/nlab/show/DHR+superselection+theory#RepresentationsFromEndomorphismsAndViceVersa)) for why every DHR representation indeed comes from a net-endomorphism, assuming Haag duality and that the net takes values in vN algebras.

   at DHR superselection theory I have added the argument (here) for why every DHR representation indeed comes from a net-endomorphism, assuming Haag duality and that the net takes values in vN algebras.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTime2 days ago
   • PermaLink
   Author: Urs
   Format: MarkdownItexfinally added pointer to the actual original articles: * [[Sergio Doplicher]], [[Rudolf Haag]], [[John E. Roberts]]: *Fields, observables and gauge transformations I*, Commun.Math. Phys. **13** (1969) 1–23 &lbrack;[doi:10.1007/BF01645267](https://doi.org/10.1007/BF01645267)&rbrack; * [[Sergio Doplicher]], [[Rudolf Haag]], [[John E. Roberts]]: *Fields, observables and gauge transformations II*, Commun. Math. Phys. **15** (1969) 173–200 &lbrack;[doi:10.1007/BF01645674](https://doi.org/10.1007/BF01645674)&rbrack; and related to [[particle statistics]] in view of [[causal locality]]: * [[Sergio Doplicher]], [[Rudolf Haag]], [[John E. Roberts]]: *Local observables and particle statistics I*, Commun.Math. Phys. **23** (1971) 199–230 &lbrack;[doi:10.1007/BF01877742](https://doi.org/10.1007/BF01877742), [euclid:cmp/1103857630](https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-23/issue-3/Local-observables-and-particle-statistics-I/cmp/1103857630.full)&rbrack; * [[Sergio Doplicher]], [[Rudolf Haag]], [[John E. Roberts]]: *Local observables and particle statistics I*, Commun.Math. Phys. **35** (1974) 49–85 &lbrack;[doi:10.1007/BF01646454](https://doi.org/10.1007/BF01646454)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/DHR+superselection+theory/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/DHR+superselection+theory/15">v15</a>, <a href="https://ncatlab.org/nlab/show/DHR+superselection+theory">current</a>

   finally added pointer to the actual original articles:

   • Sergio Doplicher, Rudolf Haag, John E. Roberts: Fields, observables and gauge transformations I, Commun.Math. Phys. 13 (1969) 1–23 [doi:10.1007/BF01645267]

   • Sergio Doplicher, Rudolf Haag, John E. Roberts: Fields, observables and gauge transformations II, Commun. Math. Phys. 15 (1969) 173–200 [doi:10.1007/BF01645674]

   and related to particle statistics in view of causal locality:

   • Sergio Doplicher, Rudolf Haag, John E. Roberts: Local observables and particle statistics I, Commun.Math. Phys. 23 (1971) 199–230 [doi:10.1007/BF01877742, euclid:cmp/1103857630]

   • Sergio Doplicher, Rudolf Haag, John E. Roberts: Local observables and particle statistics I, Commun.Math. Phys. 35 (1974) 49–85 [doi:10.1007/BF01646454]

   diff, v15, current