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 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 nforum 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 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).

nLab > Latest Changes: Haag's theorem

Bottom of Page

1 to 7 of 7

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 18th 2011

    started Haag’s theorem, following a discussion with Todd, but am running out of time

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 18th 2011

    Thanks, Urs. When you have more time: has Haag’s theorem sometimes been viewed as a motivation for the development of AQFT?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 19th 2011

    just telegraphically:

    I rarely see AQFT texts point to Haag’s theorem in particular as a motivation, but the general context of the theorem has been a major motivation: lots of technical problems in QFT simply go away if one does not insist on forming the state spaces (hence the representations of the algebras of observables) Not the least for instance infrared problems in renormalization theory.

    The idea is not that these problems cannot be actually solved, but that solving them is additional fine-grained information that can be looked at if desired, but that need not go into the axioms, hence the basic formulation of the theory.

    I’ll try to give more details on this later.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 22nd 2017

    (years later…)

    I have added the missing cross-links between Haag’s theorem and canonical commutation relation

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 22nd 2017

    Is the \ldots in

    quantum fi…eld

    on purpose?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 22nd 2017
    • (edited Dec 22nd 2017)

    thanks for the alert. looks like an artifact from copy-and-pasting out of a pdf. I have fixed it.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2022

    I have polished-up the original references in this entry, and added pointer to:

    But looking over this entry I see that it fails to even mention the gist of Haag’s theorem, regarding interacting quantum field theories. I have added a warning on this omission at the end of the Idea-section; don’t have the nerve right now to do something about it.

    diff, v5, current

1 to 7 of 7

  1.