Related papers: On the quadratic Fock functor
The main result of this paper refers to the boundedness of the orthogonal projection $P_{\alpha}:L^{2}(\mathbb{R}^{n},d\mu_{\alpha})\rightarrow \mathcal{H}_{\alpha}^{2}, n\geq2 $ associated to the harmonic Fock space…
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…
In this paper, we characterize the $d\times d$ matrix weights $W$ on $\mathbb{C}^n$ such that the Fock projection $P_{\alpha}$ is bounded on the vector-valued spaces $L^p_{\alpha,W}(\mathbb{C}^n;\mathbb{C}^d)$ induced by $W$ and the…
We study the $L^p$ norm of the orthogonal projection from the space of quaternion valued $L^2$ functions to the closed subspace of slice $L^2$ functions.
We investigate an infinite dimensional analog of the theory of Lagrangian manifolds with complex germs. To such a manifold we assign a canonical operator that depends on creation and annihilation operators. This operator is by definition…
We explicitly construct and study an isometry between the spaces of square integrable functionals of an arbitrary Levy process and a vector-valued Gaussian white noise. In particular, we obtain explicit formulas for this isometry at the…
Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the…
We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique…
It is shown that some analog of the ``second quantization'' exists in the framework of CP(N) theory. I analyse conditions under that ``geometrical bosons'' may be identified with real physical fields. The compact character of a state…
A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal…
We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the…
We derive several formulae for the spectra of the second quantization operators in abstract fermionic Fock spaces.
In this thesis, we construct a new version of orthogonal calculus for functors $F$ from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, which sends a $C_2$-representation…
Kiukas, Lahti and Ylinen asked the following general question. When is a positive operator measure projection valued? A version of this question formulated in terms of operator moments was posed in a recent paper of the present authors. Let…
The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a…
In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special…
We introduce a $q$-deformation of the Fock space of holomorphic functions on $\mathbb{C}$, based on a geometric definition of $q$-analyticity. This definition is inspired by a standard construction in complex differential geometry. Within…
The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator…
Following the prequel work \cite{VO3}, we prove a generalization of "Mazur's conjecture" for $L$-functions of elliptic curves in abelian extensions of imaginary quadratic fields, including the assertion that the Mordell-Weil rank of an…
The reduced k-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of k-body observables. A proper…