Let us split our Hilbert space into two isomorphic pieces with respect to the above decomposition of the complex structure, W ⊕ ˜W , and complexify the real Hilbert space, naturally we have W ⊗ C ⊕ ˜W ⊗ C.
Large N limit of SO(N) gauge theory of fermions and bosons
If A has a real structure, we can start with a representation of AR on a real Hilbert space HR and then complexify.
The Range of United K-Theory
When K = R, we may also view X as a holomorphic (i.e. complex analytic) vector ﬁeld by complexifying it.
Convergence versus integrability in Poincare-Dulac normal form
More generally, any Coxeter group can be seen as a complex reﬂection group, by complexifying the reﬂection representation.
Explicit presentations for exceptional braid groups
It is necessary to complexify 10H , just as in a supersymmetric theory.
Grand Unification with and without Supersymmetry