相关论文: Large N Expansion. Vector Models

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field…

A Lagrangean and a set of Feynman rules are presented for non-relativistic QFT's with manifest power counting in the heavy particle velocity $v$. A r\'egime is identified in which energies and momenta are of order $Mv$. It is neither…

In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in $1/N$, making the $1/N$ expansion a natural testing ground for the theory of resurgence. We study in detail the…

The current generation of covariant mean-field models has had many successes in calculations of bulk observables for medium to heavy nuclei, but there remain many open questions. New challenges are confronted when trying to systematically…

These are the commentaries for a volume of reprints of my selected papers with commentaries that I am preparing for publication by World Scientific. Contents: Preface; (1)Early Years, and Condensed Matter Physics; (2) High Energy Neutrino…

The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach…

We reply to a comment of Van Enter, Kuelske and Maes (cond-mat/0005176) on our letter "Critical Behavior of the Randomly Spin-Diluted 2-d Ising Model - A Grand Ensemble Approach", Phys. Rev. Lett. {\bf 73}, 2268-2271 (1994).

One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems…

The paper surveys some recent results concerning vector analysis on fractals. We start with a local regular Dirichlet form and use the framework of 1-forms and derivations introduced by Cipriani and Sauvageot to set up some elements of a…

This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.

A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…

We extend some equatilites in the Owen's table of normal integrals (A table of normal integrals in Communication in Statistics-Simulation and Computation, 1980). Furthermore a new probabilistic model for a vector of binary random variables…

The rapid development of quantum computer hardware has laid the hardware foundation for the realization of QNN. Due to quantum properties, QNN shows higher storage capacity and computational efficiency compared to its classical…

In the first part of this lecture, the 1/N expansion technique is illustrated for the case of the large-N sigma model. In large-N gauge theories, the 1/N expansion is tantamount to sorting the Feynman diagrams according to their degree of…

A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…

We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract…

Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…

In this thesis we investigate aspects of two problems. In the first part of this thesis, we concentrate on renormalization group methods in Hamiltonian framework. We show that the well-known coupled-cluster many-body theory techniques can…

Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…

I review recent works on the problem of inducing large-N QCD by matrix fields. In the first part of the talk I describe the matrix models which induce large-N QCD and present the results of studies of their phase structure by the standard…