Regularized trace formula of magic Gribov operator on Bargmann space

In this article, we obtain a regularized trace formula for magic Gribov operator H=λ″G+Hμ,λH=λ″G+Hμ,λ acting on Bargmann space whereG=a⁎3a3 and Hμ,λ=μa⁎a+iλa⁎(a+a⁎)a Here a   and a⁎a⁎ are the standard Bose annihilation and creation operators and in Reggeon field theory, the real parameters λ″λ″ is the magic coupling of Pomeron, μ is Pomeron intercept, λ   is the triple coupling of Pomeron and i2=−1i2=−1. By applying some abstract results of Sadovnichii–Podol'skii (2002) [23], we give the number of corrections sufficient for the existence of finite formula of the trace of concrete magic Gribov's operator.