Related papers: Large N Expansion. Vector Models
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at…
I describe the underlying physics behind the BFKL resummation and discuss some of the recent ideas and results in this field. On the theoretical side I consider the formalism in the next-to-leading logarithmic (NLL) approximation and the…
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…
Recently Drummond and Hillery [Phys. Rev.A 59, 691(1999)] presented a quantum theory of dispersion based on the analysis of a coupled system of the electromagnetic field and atoms in the multipolar QED formulation. The theory has led to the…
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel…
These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization. We present numerical results for the…
These lecture notes cover the basics of Quantum Field Theory (QFT) and peculiarities in the construction of the Electroweak (EW) sector of the Standard Model (SM). In addition, the present status, issues, and prospects of the SM are…
In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
Recent progresses using state-of-the-art experimental techniques have motivated a number of new insights on heavy fermion physics. This article gives a brief summary of the author's research along this direction. We discuss five major…
We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-$\beta_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our…
The validity of the work by Lamata et al [Phys. Rev. Lett. 98, 253005 (2007)] can be further shown by quantum field theory considerations.
Thesis includes review on the large order behaviour of perturbation theory in quantum mechanical and field theory models; generalization of the Borel summability and strong asymptotic conditions to various (including horn-shaped) regions;…