algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
A vector, hence an element of some vector space is called cyclic with respect to the action/representation of some algebra on if every element of may be obtained by acting on with some algebra element , or rather if one may always find a sequence of elements whose action on converges to the given element.
Let
be a C*-algebra;
a C*-representation of on .
Then a vector is called a cyclic vector if the image of under acting via is a dense subspace of :
The notions of cyclic vector is dual to that of separating vector with respect to the commutant , that is a vector is cyclic for iff it is separating for .
In algebraic quantum field theory the states corresponding to cyclic vectors appear as vacuum states. See Reeh-Schlieder theorem.
Last revised on December 26, 2017 at 16:47:15. See the history of this page for a list of all contributions to it.