Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1995 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1994 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Research Abstract 
The research results of our project for two academic years in 19941995 are as follows : 1. A new lagrangian way of defining the NambuJonaLasinio (NJL) model is proposed, which possesses an intrinsic ultraviolet cutoff by the higher derivative fermion kinetic term and maintains all the external gauge invariances. There we also discussed the quantization method of such a higherderivative system, current operators and chiral anomaly problems. 2. Based on the renormalization group method, the gaugeHiggsYukawa system was analyzed whether it is nontrivial or not ; namely, whether it can give a welldefined interacting theory when the ultraviolet cutoff goes to infinity. We proved that it is nontrivial under the following conditions : i) there exists an asymptotically free gauge interaction, whose approach to the asymptotic freedom should not be so rapid, ii) the Yukawa coupling should be smaller than or equal to an upperbound, and iii) the scalar quartic coupling is not an independent parameter but is uniquely determined by the Yukawa and gauge coupling constants. Based on the result, the gauged NJL model is proved to be renormalizable in four dimensions. 3. The procedure was clarified how one can obtain the physical Smatrix from the gaugeinvariant effective action in the background field (BF) method. We gave a precise proof that it gives the same Smatrix as the one obtained by the usual nongaugeinvariant (BRS invariant) effective action. 4. We found a new relation 1+u=Z_1/Z_3=Z_<vertex>/Z_<wavefunction>, where the lefthand side is the quantuty that 1+u = 0 is known to give a sufficient condition for the color confinement to occur, and the righthand side stands for the ratio of the renormalization factors, Z_<vertex>/Z_<wavefunction>, which is universal (i.e., matterindependent),
