iBet uBet web content aggregator. Adding the entire web to your favor.
Link to original content: http://ncatlab.org/nlab/show/Haag–Łopuszański–Sohnius theorem
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
superalgebra and (synthetic ) supergeometry
The Coleman-Mandula theorem says that the only possible symmetry Lie algebra of the S-matrix of a 4-dimensional quantum field theory with mass gap is a direct sum of the Poincare Lie algebra and some other Lie algebra of internal gauge symmetries, hence that there cannot be a non-trivial mixing between the spacetime symmetry and the internal symmetry at the level of Lie algebras and in the presence of a mass gap.
(This applies to fundamental local symmetry of the S-matrix, not to global symmetry after spontaneous symmetry breaking.)
The theorem of Haag–Łopuszański–Sohnius 75 makes the analogous statement for super Lie algebras: the only possible super Lie algebra symmetry of an S-matrix is a direct sum of the super Poincare Lie algebra (“supersymmetry”) and another super Lie algebra.
Notice that the super Poincare Lie algebra itself does mix the plain bosonic Poincare Lie algebra symmetry with a kind of “internal” symmetry, see also at extended supersymmetry.
The original article:
On the history of the result:
See also:
Last revised on September 18, 2021 at 04:42:46. See the history of this page for a list of all contributions to it.