Hilbert-space-valued states on quantum logics
How small is the phase space in quantum field theory ?
Infrared catastrophe in a massless Feynman function
Le papillon de Hofstadter
Lower bounds for Schrödinger operators in H¹(ℝ)
We prove trace inequalities of type where , under suitable hypotheses on the sequences and , with the first sequence increasing and the second bounded.
Macroscopic limiting dynamics of a class of inhomogeneous mean field quantum systems
Modular covariance, PCT, spin and statistics
N-dimensional affine Weyl-Heisenberg wavelets
On charged fields with group symmetry and degeneracies of Verlinde's matrix S*
On complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On the infrared problem in a model of scalar electrons and massless, scalar bosons
On the problem of defining a specific theory within the frame of local quantum physics
On the use of modular groups in quantum field theory
On two reverse inequalities in the Segal-Bargmann space.
Orthogonal Forms and Probability in von Neumann Algebras.
Path integrals in finite sets
Phase space properties of local observables and structure of scaling limits
Q-adapted quantum stochastic integrals and differentials in Fock scale
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field , of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone (Q = O) quantum...
Quantum Itô B*-algebras, their classification and decomposition
A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra, is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and thermal quantum noise are characterized. It is proved that every Itô algebra is canonically decomposed...
Quantum random walk revisited
In the framework of the symmetric Fock space over L²(ℝ₊), the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied. Then this result is used to prove the strong convergence of a quantum random walk as a map from an initial algebra 𝓐 into 𝓐 ⊗ ℬ (Fock(L²(ℝ₊))) to a *-homomorphic quantum stochastic flow.