|Budget Amount *help
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1991 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1990 : ¥900,000 (Direct Cost : ¥900,000)
1. As a particular property of string, there is " target space duality" : for instance, the physics of the string on a torus space compe(ctified with radius R is the same as that on a torus with radius 1/R. This duality transformation R -> 1/R is known to be extended to the group 0(d, d ; Z)for the d-dimensional torus. I have shown in collaboration with B. Zwiebach that this 0(d, d ; Z)duality is essentially contained in the string field theory as a symmetry corresponding to particular gauge transformations.
2. The fact is well-known that the pure gravity in 3 dimension is renormalizable. I have shown that the 3 dimensional gravity remains renormalizable even when matter fields are coupled to it, using 1IN expansion where N is the number of the matter fields. However, it turned out that a tachyon pole in the graviton propagator appears there. This implies that the used vacuum is unstable. I am still studying the implications and the method how to avoid this problem.
3. In collaboration w
ith Aoki, Bando and Mitchard, I have devised a method to cilcixlate the pion decay constant fpi using Higashijima, s improved ladder approximaiton to Bethe-Salpeter(BS)equation. We found that the Pagels-Stoker's approximate formula gives a rather good value for fpi. Using the similar approximaiton to BS equation, we also calculated the masses and decay constants of the lowest lying mesons in QCD such as rho, Ai and scalar mesons. The numerical results are found to reproduce the observed values surprisingly well. It was, however, discovered very receraly that the Higashijima approximation violates the chiral Ward-Takahashi(WT)identity. I have shown together with Michard that the chiral WT identity is preserved if the gluon momentum is used as the argument of the running coupling constant, and that it is necessary to use a non-local gauge with gauge parameter being a function of momentum in order for the scheme to be consistent with the ladder approximation. We have also confirmed that this consistent ladder approximation with non-local gauge reproduces almost the same numerical results for the physical quantities previously calculated.
3.青木,坂東,Mitchardらと共同で,QCDに於けるπ中間子の崩壊定数を,東島近似のBetheーSalpeter方程式で用いてより厳密に求める方法を考案し,それまで知られていたPagelsーStokerの近似式がかなり良い近似を与えることを明らかにした。また同様な近似BS方程式を用いて,QCDのP,A_1,スカラ-,メソンの質量や崩壊定数を数値的に求め,それらが驚くほど良く実験値を再現することを見出した。しかし最近,東島近似がカイラルWardー高橋(WT)恒等式を破っている事が発見され,私はMitchardと共同で,running結合定数の引数にgluon運動量を用いればカイラルWT恒等式を満たすこと,更に,Ladder近似と無矛盾にするには,ゲ-ジ・パラメ-タを運動量の関数にする非局所ゲ-ジをとる必要がある事を明らかにした。また,この非局所ゲ-ジの無矛盾なLadder BS方程式を用いた数値計算は,以前の結果と殆んど同じ数値と再現する事を確めた。 Less