-complex approximation of quantum state spaces in QAT
Let be a complete sequence of commuting quantum spin ‘foams’ (QSFs) in an arbitrary quantum state space (QSS) (http://planetmath.org/QuantumSpaceTimes), and let be the corresponding sequence of pair subspaces of QST. If is a sequence of CW-complexes such that for any , , then there exists a sequence of -connected models of and a sequence of induced isomorphisms for , together with a sequence of induced monomorphisms for .
The -connected models of form the Model Category of
Quantum Spin Foams (http://planetmath.org/SpinNetworksAndSpinFoams) , whose morphisms are maps such that , and also such that the following diagram is commutative:
Furthermore, the maps are unique up to the homotopy rel , and also rel .
Theorem 1 complements other data presented in the parent entry on QAT (http://planetmath.org/QuantumAlgebraicTopology).
|Title||-complex approximation of quantum state spaces in QAT|
|Date of creation||2013-03-22 18:14:37|
|Last modified on||2013-03-22 18:14:37|
|Last modified by||bci1 (20947)|
|Synonym||quantum spin networks approximations by -complexes|
|Defines||-complex approximation of quantum state spaces in QAT|