Related papers: Power counting in the spectral action matrix model

In the arena of the discrete phase space and continuous time, the theory of S-marix is formulated. In the special case of Quantum-Electrodynamics (QED), the Feynman rules are precisely developed. These rules in the fourmomentum turn out to…

The R*-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to…

We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes…

The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address…

Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…

We describe the Feynman rules for the construction of the Dimensionally Reduced Action (DRA) for a phi^4 field theory, as well as rules for the construction of the connected Green functions and the Dimensionally Reduced Effective Action…

On the half line $[0,\infty)$ we study first order differential operators of the form $B 1/i d/(dx) + Q(x)$, where $B:=\mat{B_1}{0}{0}{-B_2}$, $B_1,B_2\in M(n,\C)$ are self--adjoint positive definite matrices and $Q:\R_+\to M(2n,\C)$,…

Let X_1 ,..., X_n be a collection of binary valued random variables and let f : {0,1}^n -> R be a Lipschitz function. Under a negative dependence hypothesis known as the {\em strong Rayleigh} condition, we show that f - E f satisfies a…

Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…

In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…

We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.

We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with $\delta$-functions. We consider both equal and generic masses. There are three types…

The generating series of the intersection numbers of the stable cohomology classes on moduli spaces of curves satisfies the string equation and a KdV hierarchy. Kontsevich's original proof of this result uses a matrix model and the matrix…

We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent…

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…

We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a…

Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: i) starting from the low-energy effective Lagrangian and ii) starting from a random matrix theory with the…

Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum…

We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are…

In this paper the Planck function is derived in the frequency domain using the method of oscillators. It is also presented in the wavelength domain and in the wave number domain. The latter is mainly used in spectroscopy for studying…