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We consider the partition function $$ Z = \int {\cal D}A {\rm e}^{-S_b[A]} Z_f[A] $$ where $$ Z_f[A] = \int {\cal D}\psi{\cal D}\bar\psi {\rm e}^{-S_f[A,\psi,\bar\psi]} $$ Ελληνικά: Θεωρούμε τη συνάρτηση κατανομής \( \rho(x)\) και \( \rho^{(0)}(x)\) $$ \rho(x) = \langle \delta(x-\tilde\lambda) \rangle $$ $$ \rho^{(0)}(x) = \langle \delta(x-\tilde\lambda) \rangle_0 $$ where the last vev is taken wrt \( Z_0 = \int {\cal D}A {\rm e}^{-S_0[A]} \), \(S_0[A]=S_b[A]-\ln|Z_f[A]|\).
Define your own macros: $$ \rho=\ket\psi\bra\psi \qquad \vev{\bar\psi\psi} \qquad \braket{\bar\psi}{\psi} $$
Try a matrix: $$ A = \left( \begin{array}{c c c} \lambda_1 & 0 & 0 \\ 0 & \lambda_2 & 0 \\ 0 & 0 & \lambda_3\\ \end{array} \right) $$ and a piecewise smooth function: \begin{equation} |x| = \left\{ \begin{array}{l l} x & x \ge 0\\ -x & x < 0\\ \end{array} \right. \end{equation} Try eqnarray: \begin{eqnarray} x &=& 2\\ y &=& -2\\ \end{eqnarray}
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