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- W1909647598 abstract "In J. Math. Anal. App. 305. (2005), we have considered the Gribov $H_{lambda'} = lambda' S + H_{mu,lambda}$ acting on Bargmann space where $ S = a^{*2} a^{2}$ and $ H_{mu,lambda} =mu a^* a + i lambda a^* (a+a^*)a$ with $i^{2} = -1$. Here $a$ and $a^{*}$ are the standard Bose annihilation and creation operators satisfying the commutation relation $[a, a^{*}] = I$. In Reggeon field theory, the real parameters $lambda{'}$ is the four coupling of Pomeron, $mu$ is Pomeron intercept, $lambda$ is the triple coupling of Pomeron and $i^{2} = -1$. We have given an approximation of the semigroup $e^{-tH_{lambda'}}$ generated by the operator $H_{lambda'}$. In particulary, we have obtained an estimate approximation in trace norm of this semigroup by the unperturbed semigroup $e^{-tlambda'S}$. In {bf[12]}, we have regularized the operator $H_{mu,lambda}$ by $lambda''G$ where $G = a^{*3} a^{3}$, i.e we have considered $H_{lambda''} = lambda'' G + H_{mu,lambda}$ where $lambda''$ is the {it magic coupling} of Pomeron. In this case, we have established an exact relation between the degree of subordination of the non-self-adjoint perturbation operator $H_{mu,lambda}$ to the unperturbed operator $G$ and the number of corrections necessary for the existence of finite formula of the regularized trace. The goal of this article consists to study the trace of the semigroup $e^{-tH_{lambda''}}$, in particular to give an asymptotic expansion of this trace as $t rightarrow 0^{+}$." @default.
- W1909647598 created "2016-06-24" @default.
- W1909647598 creator A5040076631 @default.
- W1909647598 date "2013-11-12" @default.
- W1909647598 modified "2023-09-27" @default.
- W1909647598 title "On regularized trace formula of Gribov semigroup genrated by the Hamiltonian of reggeon field theory in Bargmann representation" @default.
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