Brazilian Journal of Physics

Non Relativistic Limit in QFT: a Wilson Renormalization Group Approach in the Minkowski Space

A. J. da Silva

Published Jun 1, 2001• 1 citation

Abstract

We study the non relativistic limit of a model of fermions interacting through a Chern-Simons field, from a perspective that resembles the Wilson Renormalization Group (WRG) approach. The main difference of our approach to WRG is that instead of working in the Euclidean space, we directly work in Minkowski space. For the nonrelativistic limit this procedure admits a more direct interpretation of the results. As we will see, this modified WRG approach solves some difficulties, and gives a new understanding of non relativistic models that are not clear in the usual "classical" nonrelativistic (CNR) limit found in most text books. The method is general and our choice of the Chern-Simons as the gauge field is only for the sake of simplicity of illustration.

DOI: 10.1590/s0103-97332001000200006

Related papers

Non relativistic limit of a Model of Fermions interacting through a Chern-Simons field

A. J. da Silva

We study the non relativistic limit of a Model of Fermions interacting through a Chern-Simons Field, from a perspective that resembles the Wilson’s Renormalization Group approach, instead of the more usual approach found in most texts of Field Theory. The solution of some difficulties, and a new understanding of non relativistic models is given.

arXiv:hep-th/9904154AIP conference proceedingsJan 1, 19990 citations

Tricritical behavior in a Chern-Simons gauge field theory

S. Sakhi

I describe a condensed matter system in terms of interacting quantum fields. In this electronic system, gauge interactions of non electromagnetic origin are generated effectively with a topological term in the effective action and play a leading role in describing the physics. Using the renormalization group and large-N expansion technique, I analyze the low energy sector of a U (1) × U (1) model in three dimensional space-time with a potential of sixth order in the scalar fields coupled to mixed Chern-Simons gauge fields. From the quantum effective potential, I derive various renormalization group functions and the fixed points associated with a quantum phase transition.

Journal of Physics Conference SeriesOct 1, 20190 citations

Whither the Anyon ?

C. R. Hägen

Abstract It is pointed out that Chern-Simons field theories do not always allow an interpretation in terms of anyons even in the nonrelativistic limit. Significantly, when the two approaches are found to differ the former is the one which is compatible with established physical principles. Thus the role left for the anyon is that of a very special subcase of Chern-Simons theories in the limit in which relativistic and spin considerations become irrelevant.

Zeitschrift für Naturforschung AFeb 1, 19971 citation

Phase Transitions and Renormalization Group

Jean Zinn‐Justin

This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, the book emphasizes the role of gaussian distributions and their relations with the mean field approximation and Landau′s theory of critical phenomena. The book shows that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. The book assigns this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range, interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process; that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. The book discusses the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, the book constructs a general functional renormalization group, which can be used when perturbative methods are inadequate.

Oxford University Press eBooksJul 5, 2007208 citations

Renormalization group ontology in quantum foundations: a non-interacting spin-0 toy model

Gary Kapilevich

A realist, anti-psi interpretation of quantum field theory is introduced, based on an expanded ontology that was inspired by the renormalization group. A goal will be to work with a classical non-interacting scalar field "toy model" in the canonical ensemble and show that an observer in this expanded ontology, under certain limiting conditions, will see a QFT. The inverse renormalization group (IRG) will be key in both interpreting this expanded ontology and furnishing novel examples of QFTs. This will lead to a definition of Planck's constant that flows as we head towards a fixed point, is expressed in terms of a temperature, and depends on the observer being studied in this expanded ontology. Our hope is that this approach will lead both to insights into quantum foundations and to prescriptions for developing new QFTs.

quant-pharXiv:2608.19458Aug 21, 20260 citations

Aspects of the renormalization group in three-dimensional quantum field theory

Benjamin R. Safdi

The concept of renormalization group (RG) flow is one of the most novel and broad-reaching aspects of quantum field theory (QFT). The RG flow is implemented by constructing effective descriptions of a QFT at decreasing energy scales. One reason that RG flow is useful is that often one is interested in low-energy properties of theories with complicated short-distance structures. RG flows are subject to C theorems in relativistic QFT. The C theorems order the space of Lorentz-invariant QFTs. RG flows generically begin at scale-invariant fixed points known as conformal field theories (CFTs) and end in trivial massive theories. With tuning, the RG flows may end at non-trivial CFTs. Each CFT has an associated dimensionless C value. The C theorem states that under RG flow from a UV to an IR fixed point, the C value decreases. In this Dissertation I present the F-theorem, which is a C theorem in three spacetime dimensions. I show that the correct quantity to consider is the Euclidean free energy of the CFT conformally mapped to the three-sphere, known as the F value. After motivating the F-theorem, I develop tools for calculating the F value in a variety of CFTs, with and without supersymmetry, including free field theories and gauge theories with large numbers of flavors. I also show that the F value is itself a useful quantity for probing the gauge/gravity duality and understanding other aspects of CFT, such as the scaling dimensions of monopole operators. The F theorem is closely related to quantum entanglement entropy. At conformal fixed points, the F value is equal to minus the renormalized entanglement entropy (REE) in flat Minkowski space across a circle. Away from the fixed points, the REE is a monotonically decreasing function along the RG flow. I compute the REE in a variety of holographic and non-holographic theories. I conclude the Dissertation by discussing a somewhat surprising result: the REE is not stationary at conformal fixed points.

Sep 25, 20140 citations