Related papers: Fermions and the Renormalisation Group at Large N
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
We study the low energy effective theory for a non-Fermi liquid state in 2+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with N flavors of fermion in the large N limit. In the low energy limit,…
We show how certain long-range models of interacting fermions in $d+1$ dimensions are equivalent to $U\left(1\right)$ gauge theories in $D+1$ dimensions, with the dimension $D$ in which gauge fields are defined larger than the dimension $d$…
We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the…
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
Quantum Chromodynamics in two spacetime dimensions is investigated with the Functional Renormalization Group. We use a functional formulation with covariant gauge fixing and derive Renormalization Group flow equations for the gauge…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
We investigate the Fermi Liquid theory of high density QCD. Using the renormalization group (RG), we determine the behavior of effective fermion interactions near the Fermi surface. At sufficiently high densities the matching between the…
We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in…
Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at…
I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the…
We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction…
The development of the Exact Renormalization Group for fermionic theories is presented, together with its application to the chiral Gross-Neveu model. We focus on the reliability of various approximations, specifically the derivative…
The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal…
A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self--energy effects…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in $D$ dimension with exponential interactions, such as $\mu^D\exp(\alpha\phi)$. In particular, we use the relation $$…
A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion…