Consistent Histories - Consistency

Consistency

An important construction in the consistent histories approach is the class operator for a homogeneous history:

The symbol indicates that the factors in the product are ordered chronologically according to their values of : the "past" operators with smaller values of appear on the right side, and the "future" operators with greater values of appear on the left side. This definition can be extended to inhomogeneous histories as well.

Central to the consistent histories is the notion of consistency. A set of histories is consistent (or strongly consistent) if

for all . Here represents the initial density matrix, and the operators are expressed in the Heisenberg picture.

The set of histories is weakly consistent if

for all .