arXiv subjects
Publications and source records attributed to Toshimitsu Takaesu.
A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists, its multiplicity is finite.
The system of a particle interacting with a Bose field is investigated. It is proven that the binding condition holds by the decay of particle's potential. As an application, the exponential decay of the ground state follows.
In this paper, we investigate the $ϕ^4$ model with cutoffs. By introducing a spatial cutoff and a momentum cutoff, the total Hamiltonian is a self-adjoint operator on a boson Fock space. Under regularity conditions of the momentum cutoff, we obtain the first order expansion of a non-degenerate ground state energy of the total Hamiltonian.
The system of semi-relativistic particles coupled to a scalar Bose field is considered. A scaled total Hamiltonian for the system is a self-adjoint operator on a tensor product of a square-integrable function space and a boson Fock space. We consider the strong resolvent limit of a renormalized Hamiltonian, which is defined by subtracting a divergent term from the scaled total Hamiltonian. Applying an abstract scaling limit theory and a unitary transformation, we derive the Yukawa potential and Coulomb potential as effective potentials.
In this paper, we consider a system of a massless Klein-Gordon field coupled to a static source. The total Hamiltonian is a self-adjoint operator on a boson Fock space. We consider annihilation operators in the Heisenberg picture and define a sesquilinear form. Under infrared regularity conditions, it is proven that the sesquilinear form is a solution of the classical field equation.
In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is defined on a tensor product of a fermion Fock space and a boson Fock. It is shown that, under spatially localized conditions and momentumregularity conditions, the total Hamiltonian has a ground state for all values of coupling constants. In particular, its multiplicity is finite.
In this article, the self-adjoint extensions of symmetric operators satisfying anti-commutation relations are considered. It is proven that an anti-commutative type of the Glimm-Jaffe-Nelson commutator theorem follows. Its application to an abstract Dirac operator is also considered.
An interaction system of a fermionic quantum field is considered. The state space is defined by a tensor product space of a fermion Fock space and a Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint operator on the state space and bounded from below. Then it is proven that a subset of real numbers is the essential spectrum of the total Hamiltonian. It is applied to the system of a Dirac field coupled to a Klein-Gordon field. Then the HVZ theorem for the system is obtained.
In this paper the system of a semi-relativistic particle interacting with a scalar Bose field is investigated. The ultraviolet cutoff condition is imposed on the Bose field. In the main theorem, the functional integral representation of the semi group generated by the total Hamiltonian with $P(ϕ)$ interaction is obtained.
We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.
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.
In this paper the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. We define a scaled total Hamiltonian and consider its asymptotic behavior. In the main theorem, it is shown that the scaled total Hamiltonian converges to a self-adjoint operator in the strong resolvent sense, and effective potentials are derived.
In this paper the Hamiltonian for the system of semi-relativistic particles interacting with a scalar bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then the semi-relativistic Schrodinger operator with an effective potential is derived.
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.
In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The spectral scattering theory is studied as well and it is shown that asymptotic fields exist and the spectral gap is closed.