arXiv subjects

Takehisa Fujita

Publications and source records attributed to Takehisa Fujita.

At least 19 recordsLinked to original sources

arXiv2018

Path integral and Sommerfeld quantization

The path integral formulation can reproduce the right energy spectrum of the harmonic oscillator potential, but it cannot resolve the Coulomb potential problem. This is because the path integral cannot properly take into account the boundary condition, which is due to the presence of the scattering states in the Coulomb potential system. On the other hand, the Sommerfeld quantization can reproduce the right energy spectrum of both harmonic oscillator and Coulomb potential cases since the boundary condition is effectively taken into account in this semiclassical treatment. The basic difference between the two schemes should be that no constraint is imposed on the wave function in the path integral while the Sommerfeld quantization rule is derived by requiring that the state vector should be a single-valued function. The limitation of the semiclassical method is also clarified in terms of the square well and $δ(x)$ function potential models.

physics.gen-ph↗

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

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↗

arXiv2011

Electric Dipole Moments of Neutron-Odd Nuclei

The electric dipole moments (EDMs) of neutron-odd nuclei with even protons are systematically evaluated. We first derive the relation between the EDM and the magnetic moment operators by making use of the core polarization scheme. This relation enables us to calculate the EDM of neutron-odd nuclei without any free parameters. From this calculation, one may find the best atomic system suitable for future EDM experiments.

nucl-th↗

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↗

arXiv2008

Quantum Gravity without General Relativity

The quantum field theory of gravitation is constructed in terms of Lagrangian density of Dirac fields which couple to the electromagnetic field $A_μ$ as well as the gravitational field $\cal G$. The gravity appears in the mass term as $ m(1+g {\cal G}) \barψψ$ with the coupling constant of $g$. In addition to the gravitational force between fermions, the electromagnetic field $A_μ$ interacts with the gravity as the fourth order effects and its strength amounts to $α$ times the gravitational force. Therefore, the interaction of photon with gravity is not originated from Einstein's general relativity which is entirely dependent on the unphysical assumption of the principle of equivalence. Further, we present a renormalization scheme for the gravity and show that the graviton stays massless.

physics.gen-ph↗

arXiv2008

Critical Review of Path Integral Formulation

The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the field theory path integral in terms of many dimensional integrations over fields does not correspond to the field quantization. We clarify the essential difference between Feynman's original formulation of path integral in QED and the modern version of the path integral method prevailing in lattice field theory calculations, and show that the former can make a correct second quantization while the latter cannot quantize fields at all and its physical meaning is unknown.

hep-th↗

arXiv2007

Bosons after Symmetry Breaking in Quantum Field Theory

We present a unified description of the spontaneous symmetry breaking and its associated bosons in fermion field theory. There is no Goldstone boson in the fermion field theory models of Nambu-Jona-Lasinio, Thirring and QCD$_2$ after the chiral symmetry is spontaneously broken in the new vacuum. The defect of the Goldstone theorem is clarified, and the "massless boson" predicted by the theorem is virtual and corresponds to just a $free$ massless fermion and antifermion pair. Further, we discuss the exact spectrum of the Thirring model by the Bethe ansatz solutions, and the analytical expressions of all the physical observables enable us to understand the essence of the spontaneous symmetry breaking in depth. Also, we examine the boson spectrum in QCD$_2$, and show that bosons always have a finite mass for $SU(N_c)$ colors. The problem of the light cone prescription in QCD$_2$ is discussed, and it is shown that the trivial light cone vacuum is responsible for the wrong prediction of the boson mass.

hep-th↗

arXiv2006

Physics of Renormalization Group Equation in QED

It is shown that the renormalization group (RG) equation in QED can only describe the finite size effects of the system. The RG equation is originated from the response of the renormalized coupling constant for the change of the system size $L$. The application of the RG equation to the continuum limit treatment of the lattice gauge theory, therefore, does not make sense, and the well-known unphysical result of the lattice gauge theory with Wilson's action cannot be remedied any more.

hep-th↗

arXiv2005

Problems of Real Scalar Klein-Gordon Field

We examine the negative energy solution in Klein-Gordon equation in terms of the number of field components. A scalar field has only one component, and there is no freedom left for an anti-particle since the Klein-Gordon equation failed to take the negative energy solution into account. This is in contrast to the Dirac equation which has four components of fields. It is shown that the current density for a real scalar field is always zero if the field is classical, but infinite if the field is quantized. This suggests that the condition of a real field must be physically too strong.

hep-th↗

arXiv2005

No Area Law in QCD

Wilson's area law in QCD is critically examined. It is shown that the expectation value of the Wilson loop integral $ \exp(\int iA_μdx^μ) $ in the strong coupling limit vanishes when we employ the conjugate Wilson action which has a proper QED action in the continuum limit. The finite value of Wilson loop with the Wilson action is due to the result of the artifact. The fact that his area law is obtained even for QED simply indicates that the area law is unphysical.

hep-th↗

arXiv2005

Nucleon Edm from Atomic Systems and Constraints on Supersymmetry Parameters

The nucleon EDM is shown to be directly related to the EDM of atomic systems. From the observed EDM values of the atomic Hg system, the neutron EDM can be extracted, which gives a very stringent constraint on the supersymmetry parameters. It is also shown that the measurement of Nitrogen and Thallium atomic systems should provide important information on the flavor dependence of the quark EDM. We perform numerical analyses on the EDM of neutron, proton and electron in the minimal supersymmetric standard model with CP-violating phases. We demonstrate that the new limit on the neutron EDM extracted from atomic systems excludes a wide parameter region of supersymmetry breaking masses above 1 TeV, while the old limit excludes only a small mass region below 1 TeV.

hep-ph↗

arXiv2004

Microscopic Calculations of Nuclear EDM

We carry out the microscopic calculations of the atomic EDM in deuterium, Xe and Hg atomic systems. Due to Schiff's theorem, we obtain the atomic EDM only from the finite nuclear size effects, but it is found that the atomic EDM is appreciably larger than expected. This is essentially due to the new mechanism in which the nuclear excitations are taken into account while atomic states stay in the ground state. The EDM of deuterium is found to be $d_D \simeq 0.017 d_n$ while the EDM of Xe and Hg become $d_{\rm Xe} \simeq 1.6 d_n$ and $d_{\rm Hg} \simeq -2.8 d_n$, respectively. It turns out that the new constraint on the neutron EDM becomes $d_n \simeq (0.37\pm 0.17 \pm 0.14)\times 10^{-28} {\rm e}\cdot {\rm cm}$.

nucl-th↗

arXiv2003

Color triplet excitations in two dimensional QCD

We present a novel calculation of color triplet excitations in two dimensional QCD with SU(2) colors. It is found that the lowest energy of the color triplet excitations is proportional to the box length $L$, and can be written as ${\cal M}_C={L\over{2π}}{g^2\overπ} $. Therefore, the color triplet excited states go to infinity when the system size becomes infinity. The properties of the color triplet states such as the wave functions are studied for the finite box length.

hep-th↗

arXiv2003

Comment on "The massive Thirring model from XYZ spin chain" by Kolanovic et al

It is shown that the continuum limit of the spin 1/2 Heisenberg XYZ model is far from sufficient for the site number of 16. Therefore, the energy spectrum of the XYZ model obtained by Kolanovic et al. has nothing to do with the massive Thirring model, but it shows only the spectrum of the finite size effects.

hep-th↗