On the space of Schwartz operators in the symmetric Fock space and its dual

A long-standing problem that arises when constructing the mathematical apparatus of quantum mechanics is need to work with unbounded operators. Since space nuclear operators preconjugate for algebra all bounded operators, we can consider states a system as and observables. In this case, taking trace product operator (a state) observable) gives average value observable in fixed state. The existence such an not guaranteed. If want define observables includes naturally occurring position momentum which values are always determined, should smaller than Recently, approach has been mathematically correct implemented Hilbert H = L^2(R^N). so-called Schwarz equipped semi-norms being Frechet space, was chosen states. appeared be integral whose kernels functions belonging usual space. dual considered it really standard polynomials from products present transfer symmetric Fock F(H) over infinite dimensional separable H. We introduce Schwartz investigate white noise belong