Related papers: Auxiliary Field Loop Expansion for the Effective A…
We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail…
In this work, we study some models of scalar fields in 1+1 dimensions with non-linear self-interactions. Here, we show how it is possible to extend the solutions recently reported in the literature for some classes of nonlinear equations…
Liquid-liquid phase separation underlies phenomena ranging from protein condensate formation to the phase coexistence of synthetic polymers. Although the random phase approximation (RPA) is widely used to predict such phase behavior, its…
The auxiliary field method is a powerful technique to obtain approximate closed-form energy formulas for eigenequations in quantum mechanics. Very good results can be obtained for Schr\"odinger and semirelativistic Hamiltonians with various…
We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point…
We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…
The 1/N expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the 1/N expansion in the O(N) model by comparing…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We show the equivalence between the three approximation schemes for self-interacting (1+1)-D scalar field theories. Based on rigorous results of [1, 2], we are able to prove that the Gaussian approximation is very precise for certain limits…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
The RG equation for the effective potential in the leading log (LL) approximation is constructed which is valid for an arbitrary scalar field theory in 4 dimensions. The solution to this equation sums up the leading $\log\phi$ contributions…
We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
We study the two-point function of local operators in the critical O(N) model in the presence of a magnetic field localized on a line. We use a recently developed conformal dispersion relation to compute the correlator at first order in the…
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theory to obtain convergence results for practical adaptive…
We present a practical approach to treat static and dynamical correlation accurately in large multi-configurational systems. The static correlation is accounted for using the spin-flip approach which is well known for capturing static…
We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and $O(\lambda^2)$, the effective equation of…