Regularized trace formula of magic Gribov operator on Bargmann space

Abstract

In this article, we obtain a regularized trace formula for magic Gribov operator\\ $ H = \lambda{''}G + H_{\mu,\lambda}$ acting on Bargmann space where $$G = a^{*3}a^{3} \quad \quad and \quad \quad H_{\mu,\lambda} = \mu a^{*}a + i\lambda a^{*}(a + a^{*})a$$ Here $a$ and $a^{*}$ are the standard Bose annihilation and creation operators and in Reggeon field theory, the real parameters $\lambda{''}$ is the magic coupling of Pomeron, $\mu$ is Pomeron intercept, $\lambda$ is the triple coupling of Pomeron and $i^{2} = -1$. An exact relation is established between the degree of subordination of the perturbation operator $H_{\mu,\lambda}$ to the unperturbed operator $G$ and the number of corrections necessary for the existence of finite formula of the trace.