相关论文: Systematic Differential Renormalization to All Ord…
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on $U(1)^4$ is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of…
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to…
In classical and quantum systems, perturbation of an evolution equation is often invalidated by secular terms which diverge at late times. The diverging behavior of evolution can be remedied by various techniques of resumma- tion such as…
In this work, we introduce a new approach for constructing a renormalized and regularized Fock matrix for self-consistent field calculations. The scheme relies on second-order perturbation theory and is conceptually related to quasiparticle…
Stable reduction methods will be important in the evaluation of high-order perturbative diagrams appearing in QCD and mixed QCD-electroweak radiative corrections at the LHC. Differential reduction techniques are useful for relating…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar.…
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
This paper formulates an elementary algorithm for resolution of singularities in a neighborhood of a singular point over a field of characteristic zero. The algorithm is composed of finite sequences of Newton polyhedra and monomial…
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical…
The high order corrections to renormalon are considered. Each new type of insertions into the renormalon chain of graphs generates the correction to the asymptotics of perturbation theory of the order of $\sim 1$. However, this series of…
For scalar QED on a three-dimensional toroidal lattice with a fine lattice spacing we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to…
This paper develops a conformal renormalization scheme for compact sets $K \subset \mathbb{C}$. As one application of the conformal renormalization scheme we prove that for every isolated non-trivial connected component $E \subset K$ there…
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…
A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal…
Building on the recent derivation of a bare factorization theorem for the $b$-quark induced contribution to the $h\to\gamma\gamma$ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization…