arXiv subjects

Naohiro Kanda

Publications and source records attributed to Naohiro Kanda.

12 recordsLinked to original sources

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↗

arXiv2021

A classical mechanical model of two interacting massless particles in de Sitter space and its quantization

A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a way that the resulting, generalized action reduces to the original action in a limit that de Sitter radius goes to infinity. We analyze the Hamiltonian formulation in accordance with Dirac's prescription for constrained Hamiltonian systems and carry out its subsequent canonical quantization in coordinate representation following DeWitt. As the result, we derive a fourth-order differential wave equation for bilocal fields that, in the infinite radius limit, reproduces one obtained in the original model for Minkowski space case.

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↗

arXiv2014

Bi-Local Field in Gravitational Shock Wave Background

The particles with almost light velocity are able to be sources of the shock-wave gravity (SWG). Then, for ultra-high-energy particles, there exist two-body scatterings such that one particle is scattered from the gravitational background produced by another particle. Since the spacetime of SWG is closely related to a pp-wave solution of AdS-type background, this type of interaction is also interesting in AdS dual gauge theories. From those viewpoints, the scattering of point particles or strings by the SWG were studied. In this paper, we study the case of the bi-local models, which are simple relativistic bound systems having a close relation with specific modes of open strings. In particular, we analyze the bound-state effect on the scattering amplitudes, which describe the interaction between this model and SWG.

hep-th↗

arXiv2012

Nuclear Potential with Two Pion Exchange

We carefully calculate the nucleon-nucleon interaction due to two pion exchange processes by properly evaluating the corresponding Feynman diagrams. In the estimation, we have made no approximation, and instead, we carry out the numerical integrations of three Feynman parameters. It is found that the two pion exchange potential gives rise to the attractive force which corresponds to the effective scalar meson with its mass of $m_s\simeq 4.7 m_π$ and its strength of ${g_s^2\over 4π}\simeq 1.45 $. There is a strong isospin dependence of $(\bmτ_1\cdot \bmτ_2)^2 $ which cannot be simulated by the one boson exchange model calculations.

nucl-th↗

arXiv2011

Light-Light Scattering

For a long time, it is believed that the light by light scattering is described properly by the Lagrangian density obtained by Heisenberg and Euler. Here, we present a new calculation which is based on the modern field theory technique. It is found that the light-light scattering is completely different from the old expression. The reason is basically due to the unphysical condition (gauge condition) which was employed by the QED calcualtion of Karplus and Neumann. The correct cross section of light-light scattering at low energy of $(\fracω{m} \ll 1)$ can be written as $ \displaystyle{\frac{dσ}{dΩ}=\frac{1}{(6π)^2}\frac{α^4} {(2ω)^2}(3+2\cos^2θ+\cos^4θ)}$.

hep-ph↗

arXiv2011

A Proposal to Measure Photon-Photon Scattering

We discuss a possibility to measure the photon-photon scattering cross section at low energy in a theoretical standpoint. The cross section of photon-photon scattering at low energy can be written as $\displaystyle{{dσ\over dΩ} \simeq {α^4\over (12π)^2 ω^2} (3+2\cos^2θ+\cos^4θ)}$ with $ω$ the energy of photon. The magnitude of the cross section at $ω\simeq 1$ eV should be $10^{37}$ times larger than the prediction of Heisenberg and Euler who calculated the photon scattering by the classical picture of field theory. Due to a difficulty of the initial condition of photon-photon reaction process, we propose to first measure $γ+γ\rightarrow e^++e^- $ reaction at a few MeV before measuring $γ+γ\rightarrow γ+γ$ elastic scattering.

hep-ph↗

arXiv2011

Tomonaga's Conjecture on Photon Self-Energy

We investigate Tomonaga's conjecture that the self-energy of photon should vanish to zero. In fact, the contribution of photon's self-energy diagram violates the Lorentz invariance and therefore it is unphysical. In addition, there occurs no wave function renormalization of photon in the exact Lippmann-Schwinger equation for the vector potential and this confirms that the conjecture is correct. Further, it is shown that the gauge condition $ k_μΠ^{μν}(k) =0$ of the vacuum polarization tensor does not hold and the relation is obtained simply due to a mathematical mistake in replacing the integration variables in the infinite integral.

physics.gen-ph↗

arXiv2010

A New Relation between Lamb Shift Energies

We derive a new relation between the observed Lamb shift energies of hydrogen and muonium atoms. The relation is based on the non-relativistic description of the Lamb shift, and the proper treatment of the reduced mass of electron and target particles (proton and muon) leads to the new formula which is expressed as $\displaystyle{{ΔE^{(H)}_{2s_{1/2}}\over ΔE^{(μ)}_{2s_{1/2}}} =({1+{m_e\over m_μ}\over 1+{m_e\over M_p}})^3}$. This relation achieves an excellent agreement with experiment and presents an important QED test free from the cutoff momentum $Λ$.

quant-ph↗

arXiv2009

Novel Solution of Mercury Perihelion Shift

We present a novel solution of the Mercury perihelion advance shift in the new gravity model. It is found that the non-relativistic reduction of the Dirac equation with the gravitational potential produces the new gravitational potential of $\displaystyle{V(r)=-{GMm\over r}+{G^2M^2m^2\over 2mc^2r^2}}$. This potential can explain the Mercury perihelion advance shift without any free parameters. Also, it can give rise to the $ω-$shift of the GPS satellite where the advance shift amounts to $({Δω\over ω})_{th} \simeq 3.4\times 10^{-10}$ which should be compared to the recent observed value of $({Δω\over ω})_{exp} \simeq 4.5\times 10^{-10}$.

physics.gen-ph↗

arXiv2009

Physics of Leap Second

The physical origin of the leap second is discussed in terms of the new gravity model. The calculated time shift of the earth rotation around the sun for one year amounts to $\displaystyle{ΔT \simeq 0.621 s/ year}$. According to the data, the leap second correction for one year corresponds to $ΔT \simeq 0.63 \pm 0.03 s/ year $, which is in perfect agreement with the prediction. This shows that the leap second is not originated from the rotation of the earth in its own axis. Instead, it is the same physics as the Mercury perihelion shift. We propose a novel dating method (Leap Second Dating) which enables to determine the construction date of some archaeological objects such as Stonehenge.

physics.gen-ph↗