Approximation of the semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann space (Q1773320)

Let \(A\) and \(A^*\) be the standard annihilation and creation operators in the Bargmann space. A non-self adjoint Gribov operator is defined by \[ H_{\lambda',\mu}= \lambda' A^{*2} A^2 + \mu A^* A + i \lambda A^*(A^*+A)A, \] where \(\mu\) is the Pomeron intercept, \(\lambda'\) is a four Pomeron coupling and \(i\lambda \) an imaginary Pomeron coupling. The operator \(H_{\lambda',\mu}\) governs the Reggeon field theory. The paper under review studies the dynamic defined by \(H_{\lambda',\mu}\) through the Trotter product formula. To this end, \(H_{\lambda',\mu}\) is split into sums of either \(\lambda' A^{*2} A^2\) and \(\mu A^* A + i \lambda A^*(A^*+A)A\) or \(\lambda' A^{*2} A^2 + \mu A^* A\) and \( i \lambda A^*(A^*+A)A\). For the first case, a specific error estimation is proved. In the second case, an approximation of the dynamic semigroup is obtained. The standard Trotter formula does not work here since \(A^*(A^*+A)A\) is not the infinitesimal generator of a semigroup. The paper contains a new technique which can handle such an obstacle.