Integrable Renormalization II: the general case
نویسندگان
چکیده
We extend the results we obtained in an earlier work [1]. The cocommutative case of ladders is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decomposition of renormalization theory is derived by using the RotaBaxter double construction, respectively Atkinson’s theorem. We also outline the extension to the Hopf algebra of Feynman graphs via decorated rooted trees.
منابع مشابه
A NUMERICAL RENORMALIZATION GROUP APPROACH FOR AN ELECTRON-PHONON INTERACTION
A finite chain calculation in terms of Hubbard X-operators is explored by setting up a vibronic Harniltonian. The model conveniently transformed into a form so that in the case of strong coupling a numerical renormalization group approach is applicable. To test the technique, a one particle Green function is calculated for the model Harniltonian
متن کاملIntegrable versus Non-Integrable Spin Chain Impurity Models
Recent renormalization group studies of impurities in spin-1/2 chains appear to be inconsistent with Bethe ansatz results for a special integrable model. We study this system in more detail around the integrable point in parameter space and argue that this integrable impurity model corresponds to a non-generic multi-critical point. Using previous results on impurities in halfinteger spin chains...
متن کاملOn the Renormalization of Hamiltonian Flows , and Critical Invariant Tori
We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable xed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a xed point has a critical invariant torus. The proof is constructive and can be used for numerical computa...
متن کاملForm Factors of Exponential Operators and Exact Wave Function Renormalization Constant in the Bullough–Dodd Model
We compute the form factors of exponential operators e in the two–dimensional integrable Bullough– Dodd model (a (2) 2 Affine Toda Field Theory). These form factors are selected among the solutions of general nonderivative scalar operators by their asymptotic cluster property. Through analitical continuation to complex values of the coupling constant these solutions permit to compute the form f...
متن کامل42 0 v 3 4 O ct 1 99 9 Renormalization of twist - three operators and integrable lattice models
Renormalization of twist-three operators and integrable lattice models. Abstract We address the problem of solution of the QCD three-particle evolution equations which govern the Q 2-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g 2 (x Bj). The quark-gluon-qua...
متن کامل