Related papers: RG Equations from Whitham Hierarchy
The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
We derive a general formula for the RG improved effective (Coleman-Weinberg) potential for classically conformal models, applying it to several examples of physical interest, and in particular a model of QCD coupled via quarks to a…
It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed…
The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\alpha$ and…
A time dependent generalization of the Ginzburg -Landau Lagrangian is proposed. It contains two terms determining the time dependence and the four arbitrary scalar functions. Relevant equations, which coincide with equations following from…
We give a probabilistic interpretation for the Barnes G-function which appears in random matrix theory and in analytic number theory in the important moments conjecture due to Keating-Snaith for the Riemann zeta function, via the analogy…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO single crystals in zero magnetic field. This indicates the need for a better…
We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [{{\sc B. A. Watson}, {An And\^o-Douglas type theorem in Riesz spaces with a conditional expectation,} {\em Positivity,} {\bf 13} (2009), 543 - 558}] and a…
We sketch some of the different roles played by Whitham times in connection with averaging, adiabatic invariants, soliton theory, Hamiltonian structures, Seiberg-Witten theory, isomonodromy problems, Hitchin systems, WDVV and Picard-Fuchs…
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as…
We show that the Wilsonian formulation of the renormalization group (RG) defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This information theoretical property of the RG allows us to derive…
The Riemann Hypothesis can be reformulated as statements about the eigenvalues of certain matrices whose entries are defined in terms of the Taylor coefficients of the zeta function. These eigenvalues exhibit interesting visual patterns…
It is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be deduced from the associated systems of nonautonomous…
A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the lowest non-vanishing derivatives of theta functions with…
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…
We construct series expansions for the scaling variables (which transform multiplicatively under a renormalization group (RG) transformation) in examples where the RG flows, going from an unstable (Wilson's) fixed point to a stable…