Related papers: A Little Large N Group Theory
We present explicit formulas for the matrix elements of the SU(6) generators for totally symmetric spin-flavor states, relevant for baryon spectroscopy in large $N_c$ QCD. We rely on the interplay between two different methods to calculate…
We argue directly from Witten's analysis of large $N_c$ baryons that the structure of the $s$-wave low-spin baryon states in QCD becomes spin-independent as $N_c\rightarrow\infty$. This property leads to $SU(6)$-like behavior of static…
A spin-flavor symmetry emerges for baryons in the large-N_c limit. Large-N_c baryons form irreducible representations of the spin-flavor algebra, and their static properties can be computed in a systematic expansion in 1/N_c. Symmetry…
We derive general analytic formulae for the matrix elements of the SU(6) generators for mixed symmetric $[N_c-1,1]$ spin-flavor states with an arbitrary number $N_c$ of quarks. They are relevant for baryon spectroscopy in the $1/N_c$…
Using group theory arguments we extend and complete our previous work by deriving all SU(6) exact wave functions associated to the spectrum of mixed symmetric baryon states $[N_c-1,1]$ in the $1/N_c$ expansion. The extension to SU(6)…
These lectures are designed to introduce the methods and results of large N_c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all…
We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary…
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…
We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…
This thesis concerns the large-N limit, a classical limit where fluctuations in gauge-invariant variables vanish. The large dimension limit for rotation-invariant variables in atoms is given as an example of a classical limit other than…
Young diagrams are ubiquitous in combinatorics and representation theory. Here we explain these diagrams, focusing on how they are used to classify representations of the symmetric groups $S_n$ and various "classical groups": famous groups…
We consider two dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large…
The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N_c) color group. The problem can be formulated as a random walk of partons in the N_c-1…
Two ideas have greatly contributed to our understanding of baryon structure in the framework of Quantum Chromodynamics (QCD). The first, chiral symmetry, received its fundamental justification from QCD and has been developed into the…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete…
We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi…
The baryon spectra are discussed in the context of the $1/N_c$ expansion approach, with emphasis on mixed symmetric states. The contributions of the spin dependent terms as a function of the excitation energy are shown explicitly. At large…