CHARACTERIZATION OF PRODUCT STATES ON POLYNOMIAL ALGEBRAS IN TERMS OF SCALAR PRODUCTS OF THE ASSOCIATED n-PARTICLE VECTORS

摘要

We prove that, in the framework of generalized quantizations, orthogonality of n-particle vectors corresponding to different multi-indexes, together with an additional condition on the norms of n-particle vectors, characterizes product states. Implications of this result for the nonlinear quantization program are discussed.