Extended statistical modeling under symmetry; the link toward quantum mechanics

Extended Statistical Modeling under Symmetry; the Link toward Quantum Mechanics

We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set A of incompatible experiments, and a transformation group G on the cartesian product Π of the parameter spaces of these experiments. The set of possible parameters is constrained to lie in a subspace of Π, an orbit or a set of orbits of ...

PT symmetry in classical and quantum statistical mechanics.

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The...

Symmetry in quantum mechanics

Symmetry in quantum mechanics

Symmetry in quantum mechanics