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A pseudoscalar Yukawa interaction couples a Dirac field bilinear containing the chirality matrix to a spin-zero field. In the standard mostly-minus gamma matrix convention with ${\gamma }^5=i{\gamma }^0{\gamma }^1{\gamma }^2{\gamma }^3$ and the usual Dirac adjoint, $ig\bar{\psi }{\gamma }^5\psi \varphi$ is Hermitian for real $g$ and real $\varphi$. If $\varphi$ is a pseudoscalar, the interaction also preserves parity symmetry in quantum field theory; if $\varphi$ is parity even, it breaks that symmetry. Moving the factor $i$ into the definition of ${\gamma }^5$ changes the displayed vertex coefficient but not the interaction. Each vertex has one bosonic leg and two oppositely oriented fermion legs, and preserves Dirac fermion number conservation.

The spinor Lorentz matrices preserve the indefinite form defined by ${\gamma }^0$: $S^{†}{\gamma }^{0}S={\gamma }^0$. This follows from the gamma-matrix adjoint identities for infinitesimal generators and extends to finite connected transformations. Consequently the Dirac adjoint transforms with $S^{-1}$, even though a boost matrix is not ordinarily unitary.

For ${\gamma }_0=-i{\sigma }_1$, ${\gamma }_1={\sigma }_2$ and ${\gamma }_2={\sigma }_3$, choose $r(K_1)={\sigma }_3/2$, $r(K_2)=-{\sigma }_2/2$ and $r(J)=-i{\sigma }_1/2$. These satisfy the three-dimensional Lorentz algebra brackets and $r(T{)}^{†}{\gamma }_0+{\gamma }_{0}r(T)=0$ for real $T$. Consequently $\delta \psi =r(T)\psi$ preserves the Dirac adjoint bilinear. Its matrix is anti-Hermitian in this signature convention, so $i{\psi }^{†}{\gamma }_0\psi$ is real for ordinary commuting components.

For ${\psi }^C={\eta }_{C}C{\bar{\psi }}^T$ and ${\gamma }^{0T}={\gamma }^0=-C{\gamma }^0{C}^{-1}$, the Dirac adjoint transforms as ${\bar{\psi }}^C=-{\eta }_C^{\ast }{\psi }^T{C}^{†}$. Anticommuting the components of the fermion bilinear gives $(\bar{\psi }\psi {)}^C=\bar{\psi }(C^{†}C{)}^T\psi$. Invariance of the scalar bilinear therefore fixes $C^{†}C=I$.