阁图展开与有效势 Coleman-Weinberg厘论 Gross-Neveu模型 局域复合算管的有领势 000000●0000 00000000 0000000 o0000 W[J]Wo(J]+Wi[J]+W2[J] Wo[]=S(oa)=S(oa)+ d'x Joa W=TrIn iD-《a 6W 6W% 6S[oa]5oa(y) 5J(x) +86+a6tr-=a8 中=+p1 6WL WL=W1+W =WU-/dxJ=Slod]+/'xJeal(@a-)+W:loaj-sl3-0iJ+/dxJo.+Wl3-@] -明-器a+盟oa60-h +w[ -+o 66x) [器+-器 ∫0+a r肉=调-/y6oo0+的-/器国+o的 =T向+T向+T向+O(h) 王 动力学对称性自发破缺✽➵ ✗ãÐ♠❺❦✟➩ Coleman-Weinberg♥Ø Gross-Neveu✜✳ Û➁❊Ü➂❰✛❦✟➩ W[J] = W0[J]+W1[J]+W2[J] W0[J] = SJ (φcl) = S(φcl)+Z d 4 x Jφcl W1[J]= i 2 Tr ln iD −1 (φcl) φˆ = δW δJ δW0 δJ(x) = Z d 4 y δS[φcl] δφcl(y) δφcl(y) δJ(x) + Z d 4 y [ δφcl(y) δJ(x) J(y) + φcl(y)δ(x − y)] = φcl(x) φˆ = φcl + φ1 φ1 = δWL δJ(x) WL = W1 + W2 Γ[φˆ]=W[J]− Z d 4 xJφˆ=S[φcl]+Z d 4 x J[φcl](φcl−φˆ)+WL[φcl] = S[φˆ−φ1]+Z d 4 x Jφ1+WL[φˆ−φ1] = S[φˆ] − Z d 4 x δS[φˆ] δφˆ(x) φ1(x) + 1 2 Z d 4 xd4 y φ1(x) δS[φˆ] δφˆ(x)δφˆ(y) φ1(y) − Z d 4 x J[φcl]φ1 +WL[φˆ] − Z d 4 x δWL[φˆ] δφˆ(x) φ1(x) + O(~ 3 ) Z d 4 x " δS[φˆ] δφˆ(x) + J[φcl] # φ1(x) = Z d 4 x » δS[φcl] δφcl(x) + Z d 4 y δ 2 S[φcl] δφcl(x)δφcl(y) φ1(y) + J[φcl] – φ1(x) Γ[φˆ] = S[φˆ] − 1 2 Z d 4 xd4 y φ1(x) δS[φˆ] δφˆ(x)δφˆ(y) φ1(y) + WL[φˆ] − Z d 4 x δWL[φˆ] δφˆ(x) φ1(x) + O(~ 3 ) = Γ0[φˆ] + Γ1[φˆ] + Γ2[φˆ] + O(~ 3 ) ✜➇ (➌✉➀➷) â❢♥Ø❀❑ ➘ å ➷ é → ✺ ❣ ✉ ➺ ✧