Local exponents and infinitesimal generators of canonical transformations on Boson Fock spaces

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

A pr 2 00 7 Recursive boson system in the Cuntz algebra O ∞

Bosons and fermions are often written by elements of other algebras. M. Abe gave a recursive realization of the boson by formal infinite sums of the canonical generators of the Cuntz algebra O∞. We show that such formal infinite sum always makes sense on a certain dense subspace of any permutative representation of O∞. In this meaning, we can regard as if the algebra B of bosons was a unital ∗s...

Statistics of Composite Systems and Anyons in the Fractional Quantum Hall Effect

The commutation relations of composite fields are studied in the 3, 2 and 1 spatial dimensions. It is shown that the field of an atom consisting of a nucleus field and an electron field satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock space of the atom. The field-particle duality in the bound state is discussed from a statistical point of vi...

Ultracoherence and Canonical Transformations

Canonical transformations are studied in the bosonic Fock space using coherent and ultracoherent vectors. The connection between the Weyl operator and the homogeneous canonical transformations (Bogoliubov transformations) is presented. The unitary ray representation of the symplectic group is defined in the bosonic Fock space by the action of the group on the ultracoherent vectors.