19 We include external scalar and pseudoscalar source fields S and P , as well as scalar and pseudoscalar diquark source fields Q and R #6 as The vector and axial-vector external gauge fields V µ and A µ as well as diquark external gauge fields carrying J P = 1 + and 1 − ( B µ and D $^{µ}$) are included as These external fields satisfy the following conditions: Now, the total Lagrangian is given by where we use the following form of the gamma matrices: From the form given in Eq.(A.8) the existence of the SU (2 N$_{f}$ ) flavor symmetry is seen as follows: Since the fundamental representation of SU (2)$_{color}$ as well as that of SU (2)$_{spin}$ is the pseudreal representation, a combination of σ$_{2}$τ$_{2}$q ∗ R has the same transformation property γ$_{ν}$ =   0 ¯ σ$_{ν}$ σ$_{ν}$ 0   ≡   0 ( 1 , σ$_{j}$ ) ( 1 , − σ$_{j}$ ) 0   . (A.9) ∫ d $^{4}$x i ¯ ψ$_{i}$γ$_{ν}$D $^{ν}$ψi = ∫ d $^{4}$x ( iq † $_{L,i}$σ$_{ν}$ D $^{ν}$qi L + iq † $_{R,i}$¯ σ$_{ν}$D $^{ν}$qi R ) , (A.8) #6 Q and R are color-singlet states in two-color QCD. This can be seen from the existence of iτ$_{2}$ = ϵ and the charge-conjugation matrix C ≡ iγ$_{2}$γ$_{0}$ in Eq. (A.4). L QCD = L 0 QCD + L ext-scalar + L ext-vector . (A.7) S † = S , P † = P , ( V $^{µ}$) † = V $^{µ}$, ( A $^{µ}$) † = A $^{µ}$, Q T = −Q , R T = −R , ( B $^{µ}$)T = B $^{µ}$, ( D $^{µ}$)T = −D $^{µ}$. (A.6) L ext-scalar = ¯ ψ ( S + i P ) ψ + 1 2 [ ψ $^{T}$C ( γ$_{5}$ Q + i R ) iτ$_{2}$ψ + (h.c)] . (A.4) L ext-vector = ¯ ψγ$_{µ}$ ( V $^{µ}$− γ$_{5}$ A $^{µ}$) ψ + 1 2 [ ψ $^{T}$Cγ$_{µ}$ ( B $^{µ}$− γ$_{5}$ D $^{µ}$) iτ$_{2}$ψ + (h.c)] . (A.5) It is convenient to introduce two-component spinors q$_{L}$ and q$_{R}$ in such a way that the four-component spinor ψ is expressed as ψ i =   q i L q i R   , where i denotes the flavor index. Then, the kinetic term of quarks is rewritten as