arXiv subjects

Haruki Toyoda

Publications and source records attributed to Haruki Toyoda.

7 recordsLinked to original sources

arXiv2024

An approach to quasinormal modes of black hole based on reversed harmonic oscillator dynamics

The frequencies of quasinormal modes (QNM) for the Schwartzschild black hole are studied from the viewpoint of the particle scattering under an effective Regge-Wheeler type of potential consisting of a parabolic type one in an intermediate region and flat potentials on both sides. In particular, we use the eigenstates for a reversed harmonic oscillator as the complete bases in this intermediate region. Under this setting, the transmission and reflection coefficients are studied in addition to the frequencies of QNMs.

gr-qc↗

arXiv2021

Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect

The bi-local fields are the quantum fields of two-particle systems, the bi-local, systems, bounded by relativistic potentials. Since those form constrained dynamical systems, it is limited to introduce the interactions of the bi-local fields with other fields. In this paper, the interaction between the bi-local fields and a constant electric field $E$ is studied with consideration for the consistency of constraints. Then, we evaluate the Schwinger effect for the bi-local systems, which gives the pair production probability of the bound states as a function of the charges of respective particles and the coupling constant in the binding potential. Through this analysis, we also discuss the possibility for the dissociation of bi-local systems due to the electric field.

hep-th↗

arXiv2020

Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect

The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder operators in harmonic oscillators, though their analytic solutions are well known. In this paper, we discuss a simple algebraic way to introduce the ladder operators of the repulsive harmonic oscillators, which can reproduce well-known analytic solutions. Applying this formalism, we discuss the charged particles in a constant electric field in relation to the Schwinger effect; the discussion is also made on a supersymmetric extension of this formalism.

hep-th↗

arXiv2018

An Approach to Yukawa's Elementary Domain Based on $\mbox{AdS}_5$ Spacetime

The field equations of elementary domains proposed by Yukawa in 1968 are studied from the viewpoint of particle embedded $\mbox{AdS}_5$ spacetime with warp factor. The fifth dimension in $\mbox{AdS}_5$ is known to produce the branes associated with the energy hierarchy as a effect of the warp factor. The particles embedded in this spacetime behave as those in an infinite square well potential due to the boundary conditions in the fifth dimension. Then the superposition of the fields for those particles leads to a Yukawa's domain type of difference equation under some conditions. As a new perspective on AdS spacetime, we investigate the mechanisms that lie between the domain type of field equations in this sense and the spacetime with a compact extra dimension in detail.

hep-th↗

arXiv2016

Bi-Local Fields in AdS${}_5$ Spacetime

Recently, the bi-local fields attract the interest in studying the duality between $O(N)$ vector model and a higher-spin gauge theory in AdS spacetime. In those theories, the bi-local fields are realized as collective one's of the $O(N)$ vector fields, which are the source of higher-spin bulk fields. Historically, the bi-local fields are introduced as a candidate of non-local fields by Yukawa. Today, Yukawa's bi-local fields are understood from a viewpoint of relativistic two-particle bound systems, the bi-local systems. We study the relation between the bi-local collective fields out of higher-spin bulk fields and the fields out of the bi-local systems embedded in AdS${}_5$ spacetime with warped metric. It is shown that the effective spring constant of the bi-local system depends on the brane, on which the bi-local system is located. In particular, a bi-local system with vanishing spring constant, which is similar to the bi-local collective fields, can be realized on a low-energy IR brane.

hep-th↗

arXiv2006

q-Deformed Bi-Local Fields II

We study a way of $q$-deformation of the bi-local system, the two particle system bounded by a relativistic harmonic oscillator type of potential, from both points of view of mass spectra and the behavior of scattering amplitudes. In our formulation, the deformation is done so that $P^2$, the square of center of mass momentum, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes nonlinear with respect to $P^2$; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to the second order. The study is also made on the covariant $q$-deformation in four dimensional spacetime.

hep-th↗

arXiv2004

Q-Deformed Bi-Local Fields

We study the q-deformation of the bi-local system, two particle system, bounded by a relativistic harmonic oscillator type of potential from both points of view of mass spectra and the behavior of scattering amplitudes. In particular, we try to formulate the deformation so that $P^2$, the square of center of mass momenta, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes non-linear one with respect to $P^2$; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to second order.

hep-th↗