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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.

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