Introducing Kubo-Martin-Schwinger KMS States

Aiming to establish the fundaments of the chemical reactivity on quantum mathematical-physical concepts, a new way can be approached, by considering the statistical quantum phenomenology of the multi-electronic processes. In this context, the relationship between the Heisenberg and Schrodinger dynamic formalisms is constituted to be the starting point. 

For a multi-particles system, the canonical coordinates associated to tiie 

From the physical point of view, any vector from the Hilbert space (normalized) H = L R1, H corresponds to a system state, while 

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

In the 20s, 30s Stone and (von Neumann, 1929) have worked to clarify the connections between the two formalisms, in a coherent mathematical description, showing that the quantum theory is essentially unique. For example, in 1930, Stone (von Neumann, 1961) showed that if t 17 is a continuous unitary representation along a real line, then there is a unique self-adjoint operator for H so that will be satisfied the equation  

---