Formula_25295

\[\begin{gathered}{\left[a_{\lambda}(p), a_{\lambda^{\prime}}^{+}\left(p^{\prime}\right)\right]_{+}=\delta_{\lambda \lambda^{\prime}} \delta\left(\boldsymbol{p}-\boldsymbol{p}^{\prime}\right),} \\{\left[\tilde{a}_{\lambda}(p), \tilde{a}_{\lambda^{\prime}}^{+}\left(p^{\prime}\right)\right]_{+}=\delta_{\lambda \lambda^{\prime}} \delta\left(p-p^{\prime}\right),} \\{\left[a_{\lambda}(p), a_{\lambda^{\prime}}\left(p^{\prime}\right)\right]_{+}=\left[\tilde{a}_{\lambda}(p), \tilde{a}_{\lambda^{\prime}}\left(p^{\prime}\right)\right]_{+}=} \\=\left[a_{\lambda}(p), \tilde{a}_{\lambda^{\prime}}\left(p^{\prime}\right)\right]_{+}=0 .\end{gathered}\]