Related papers: Renormalization Group as a Koopman Operator
We consider two interacting connected graded Hopf algebras, the former being a comodule-coalgebra on the latter. We show how to define analogues of Connes-Kreimer's renormalization group and Beta function, when the graduation operator is…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological…
The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…
It is shown that the Holographic Renormalization Group can be formulated universally within Quantum Field Theory as (the quantization of) the Hamiltonian flow on the cotangent bundle to the space of gauge-invariant single-trace operators…
We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal maps of bounded type with a critical exponent which is…
We consider renormalization group (RG) transformations for classical Ising-type lattice spin systems in the infinite volume limit. Formally, the RG maps a Hamiltonian H into a renormalized Hamiltonian H': exp(-H'(\sigma'))=\sum_\sigma…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…
A block spin renormalization group approach is introduced which can be applied to dynamical triangulations in any dimension.
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…