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.Comment: 4 pages, no figur

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 $\exp(\int iA_\mu dx^\mu)$ 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.Comment: 4 pages, no figur

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 $k_\mu \Pi^{\mu \nu}(k) =0$ 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.Comment: 10 pages, no figur

No massless boson in chiral symmetry breaking in NJL and Thirring models

We show that the chiral symmetry breaking occurs in the vacuum of the massless Nambu-Jona-Lasinio (NJL) and Thirring models without a Goldstone boson. The basic reason of non-existence of the massless boson is due to the fact that the new vacuum after the symmetry breaking acquires nonzero fermion mass which inevitably leads to massive bosons. The new vacuum has a finite condensate of $$ with the chiral current conservation. Thus, it contradicts the Goldstone theorem, and we show that the proof of the Goldstone theorem cannot be justified any more for fermion field theory models with regularizations.Comment: 18 pages, two figures, Late

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 $\omega-$shift of the GPS satellite where the advance shift amounts to $({\Delta \omega\over \omega})_{th} \simeq 3.4\times 10^{-10}$ which should be compared to the recent observed value of $({\Delta \omega\over \omega})_{exp} \simeq 4.5\times 10^{-10}$.Comment: 4 page, no figure, submitted to Phys. Rev. Let

Possible Suppression of Neutron EDM

Employing generalized Schiff's transformation on electric dipole moments (EDM) in quantum field theory, we show that the chromoelectric EDM lagrangian density is transformed into the electric EDM term with a new coefficient. Under the new constraint on the EDM operators, the neutron EDM can be described by a unique combination of electric EDM $d_f$ and chromoelectric EDM ${\tilde d}_f$ of quarks. If the special relation of $\displaystyle{d_f={e_f\over{2g_s}}{\tilde d}_f}$ holds, then the neutron EDM is suppressed significantly.Comment: 9 pages, Late

Reexamination of standard solar model to the solar neutrino problems

We examine the calculation of the solar neutrino flux based on the standard solar model (SSM). It is found that the solar neutrino data (KAMIOKANDE experiment) can be well described by the SSM with careful employment of nuclear data of $^7Be (p,\gamma) ^{8} B$. The main point is that the simple-minded product ansatz of Coulomb plus nuclear parts should have a few percent uncertainties which induce the large reduction of the neutrino flux from $^8 B$. Also, if the electron capture of $^7 Be$ inside the sun is suppressed, then the GALLEX experiment can be understood by the SSM calculation.Comment: 13 pages, 2 figures, Late

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 ${\cal M}_C={L\over{2\pi}}{g^2\over{\pi}}$. 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.Comment: 10 pages, 3 figure, Late

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 $\delta(x)$ function potential models.Comment: 7 page

Violation of S-matrix factorization in massive Thirring model

We present a counter example which shows the violation of the S-matrix factorization in the massive Thirring model. This is done by solving the PBC equations of the massive Thirring model exactly but numerically. The violation of the S-matrix factorization is related to the fact that the crossing symmetry and the factorization do not commute with each other. This confirms that the soliton antisoliton S-matrix factorization picture of the sine-Gordon model is semiclassical and does not lead to a full quantization procedure of the massive Thirring model.Comment: 28 pages, Latex, 3 figures, Phys. Rev. D58 in pres