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Regularized trace formula of magic Gribov operator on Bargmann space. (English) Zbl 1332.81062
Summary: In this article, we obtain a regularized trace formula for magic Gribov operator $$H = \lambda^{\prime\prime} G + H_{\mu, \lambda}$$ acting on Bargmann space where $G = a^{\ast 3} a^3\quad \text{and}\quad H_{\mu, \lambda} = \mu a^\ast a + i \lambda a^\ast(a + a^\ast) a$ Here $$a$$ and $$a^\ast$$ are the standard Bose annihilation and creation operators and in Reggeon field theory, the real parameters $$\lambda^{\prime\prime}$$ is the magic coupling of Pomeron, $$\mu$$ is Pomeron intercept, $$\lambda$$ is the triple coupling of Pomeron and $$i^2 = - 1$$. By applying some abstract results of V. A. Sadovnichij and V. E. Podol’skij [Sb. Math. 193, No. 2, 279–302 (2002); translation from Mat. Sb. 193, No. 2, 129–152 (2002; Zbl 1033.47012)], we give the number of corrections sufficient for the existence of finite formula of the trace of concrete magic Gribov’s operator.

##### MSC:
 81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
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