Masami Wakano

Asymptotics of electromagnetic radiation off a spherical superconductor

Asymptotics of electromagnetic radiation off a spherical superconductor is analyzed in terms of creeping waves. Temporal damping behavior of the charge distribution on the surface when the sphere is rendered superconducting is studied and is compared with that on a superconductor with an infinite plane surface. Finally, the coherent states of light waves outside a spherical superconductor and a superconductor with an infinite plane surface are constructed.

Effects of the Instanton in Unified Gauge Theories

In a recent work!) of the Euclidean vacuum in quantum chromodynamics we showed that the magnetic permeability suffers an abrupt change at a certain value of t~e external color electric field. This abrupt change in the magnetic permeability continues to hold until the cutoff length of the dipolar interaction between pseudoparticles becomes small. According to Callan, Dashen and Gross the effective coupling constant might be obtained from its asymptoticfreedom value by multiplying the square root of the magnetic permeability. Therefore, if we tentatively identify the transition region in the magnetic permeability with the radius of hadrons and the width of hadrons surfaces,3) the effective coupling constant abruptly decreases as one goes from the outside to the inside of hadrons. This would explain that quarks behave as free partons inside the hadron and hadrons suffer large momentum-transfer collisions. Thus the instantons seem to be responsible for the quark confinement, so that the evidence for the effect of instantons is highly desirable. For this purpose we apply the renormalization group method to determine the asymptotic freedom value of the coupling constant of the SU(2) and SU(3) gauge fields contained in the unifying SU(5) group. Then by multiplying with the square root of magnetic permeabilities at corresponding mass scales, we can trace the instanton effect on the magnitude of effective coupling constants as mass scales are varied and see how this effect is reflected in the mass of ¢>-mesons as a strange quark-antiquark bound state. Strictly speaking, a delicate difficulty in this analysis arises from the fact that we could not calculate the average magnetic permeability experienced by a quark inside the hadron. That is, when a quark inside the hadron lies far from hadrons surfaces, the magnetic permeability with which the quark is associated should be near unity. But, when a quark lies near or almost on hadrons surfaces, the magnetic permeability felt by the quark should be close to its vacuum value without any influence of color electric fields produced by other constituent quark inside the same hadron. To the present knowledge we could not correctly take into account both together, so that, to make the result clear we consider separately the above two extreme cases, one with no instant on and the other with no suppression of instantons by color electric fields. Callan, Dashen and Gross indicated that the effective coupling constant is rei a ted with its asymptotic freedom value, at mass scale m, as follows: