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Toshimitsu Takaesu

  1. A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra.

    Wed, 07/07/2010 - 15:01 — SomNambul
    Authors: Toshimitsu Takaesu
    Subjects: Functional Analysis
    Abstract

    In this article we consider linear operators satisfying a generalized
    commutation relation of a type of the Heisenberg-Lie algebra. It is proven that
    a generalized inequality of the Hardy's uncertainty principle lemma follows.
    Its applications to time operators and abstract Dirac operators are also
    investigated.

  2. On the Essential Self-Adjointness of Anti-Commutative Operators.

    Tue, 07/06/2010 - 15:02 — SomNambul
    Authors: Toshimitsu Takaesu
    Subjects: Functional Analysis
    Abstract

    In this article, linear operators satisfying anti-commutation relations are
    considered. It is proven that an anti-commutative type of the
    Glimm-Jaffe-Nelson commutator theorem follows.

  3. Ground States of the Yukawa models with Cutoffs.

    Thu, 12/31/2009 - 16:01 — SomNambul
    Authors: Toshimitsu Takaesu
    Subjects: Functional Analysis
    Abstract

    Ground states of the so called Yukawa model is considered. The Yukawa model
    describes a Dirac field interacting with a Klein-Gordon field. By introducing
    both ultraviolet cutoffs and spatial cutoffs, the total Hamiltonian is defined
    as a self-adjoint operator on a boson-fermion Fock space. It is shown that the
    total Hamiltonian has a positive spectral gap for all values of coupling
    constants. In particular the existence of ground states is proven.

  4. Scaling Limit of Quantum Electrodynamics with Spatial Cutoffs.

    Mon, 08/17/2009 - 18:30 — SomNambul
    Authors: Toshimitsu Takaesu
    Subjects: Mathematical Physics
    Abstract

    In this paper we consider the Hamiltonian of quantum electrodynamics, which
    describes the system of Dirac fields coupled to quantized radiation fields. We
    impose ultraviolet cutoffs on the Dirac field and the radiation field, and
    introduce spatial cutoffs to define the Hamiltonian as a self-adjoint operator
    on a boson-fermion Fock space. Taking a scaling limit of the Hamiltonian, we
    derive the effective potential.

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