Multi-Instanton Effect in Two Dimensional QCD

We analyze multi-instanton sector in two dimensional U(N) Yang-Mills theory on a sphere. We obtain a contour intregrals representation of the multi-instanton amplitude and find ``neutral'' configurations of the even number instantons are dominant in the large N limit. Using this representation, we calculate 1,2,3,4 bodies interactions and the free energies for $N =3,4,5$ numerically and find that in fact the multi-instanton interaction effect essentially contribute to the large N phase transition discovered by Douglas and Kazakov.Comment: 18 pages, Latex, 3 Postscript figures; misprint corrected and several references adde

Possible Long-Range Order with Singlet Ground State in CeRu2Al10

We investigate the thermal and transport properties of CexLa1-xRu2Al10 to clarify the origin of the recently discovered mysterious phase below T0=27 K in CeRu2Al10 where a large magnetic entropy is released, however, the existence of an internal magnetic field is ruled out by 27Al-NQR measurement. We find that T0 decreases with decreasing x and disappears at x~0.45. T0 of CeRu2Al10 is suppressed down to 26 K under H=14.5 T along the a-axis. These results clearly indicate that the transition has a magnetic origin and is ascribed to the interaction between Ce ions. Considering the results of specific heat, magnetic susceptibility, thermal expansion, and electrical resistivity and also 27Al NQR, we propose that the transition originates from the singlet pair formation between Ce ions. Although its properties in a Ce dilute region is basically understood by the impurity Kondo effect, CeRu2Al10 shows a Kondo-semiconductor-like behavior. The phase transition at T0 may be characterized as a new type of phase transition that appears during the crossover from the dilute Kondo to the Kondo semiconductor.Comment: 10 pages, 5 figure

Completeness of scattering states of the Dirac Hamiltonian with a step potential

The completeness, together with the orthonormality, of the eigenfunctions of the Dirac Hamiltonian with a step potential is shown explicitly. These eigenfunctions describe the scattering process of a relativistic fermion off the step potential and the resolution of the identity in terms of them (completeness) is shown by explicitly summing them up, where appropriate treatments of the momentum integrations are crucial. The result would bring about a basis on which a field theoretical treatment for such a system can be developed.Comment: 16 pages, 1 figure