Generalized uncertainty relations and characteristic invariants for the multimode states

Abstract

The close relationship between the zero-point energy, the uncertainty relation, coherent states, squeezed states, and correlated states for one mode is investigated. This group theoretic perspective of the problem enables the parametrization and identification of their multimode generalization. A simple and efficient method of determining the canonical structure of the generalized correlated states is presented. Implication of canonical commutation relations for correlations are not exhausted by the Heisenberg uncertainty relation, not even by the Schrödinger-Robertson uncertainty inequality, but there are relations in the multimode case that are the generalization of the Schrödinger-Robertson relation.