4 papers
The first order expansion of a ground state energy of the model with cutoffs
Toshimitsu Takaesu
In this paper, we investigate the model with cutoffs. By introducing a spatial cutoff and a momentum cutoff, the total Hamiltonian is a self-adjoint operator on a boson Fock…
Construction of solutions of the classical field equation for a massless Klein-Gordon field coupled to a static source
Toshimitsu Takaesu
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…
Functional Integral Representation for Relativistic Schrodinger Operator Coupled to a Scalar Bose Field with Interaction
Toshimitsu Takaesu
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…
A Probabilistic Representation of the Ground State Expectation of Fractional Powers of the Boson Number Operator
Fumio Hiroshima, Jozsef Lorinczi, Toshimitsu Takaesu
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…