1,106 research outputs found
On the quadratic Fock functor
We prove that the quadratic second quantization of an operator p on
is an orthogonal projection on
the quadratic Fock space if and only if p =MI, where MI is a multiplication
operator by a characteristic function I.Comment: 1
The quadratic Fock functor
We construct the quadratic analogue of the boson Fock functor. While in the
first order case all contractions on the 1--particle space can be second
quantized, the semigroup of contractions that admit a quadratic second
quantization is much smaller due to the nonlinearity. Within this semigroup we
characterize the unitary and the isometric elements.Comment: 2
Extending the Set of Quadratic Exponential Vectors
We extend the square of white noise algebra over the step functions on R to
the test function space of bounded square-integrable functions on R^d, and we
show that in the Fock representation the exponential vectors exist for all test
functions bounded by 1/2
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