Quantum Hadrondynamics in Two Dimensions

Abstract

A nonlocal and nonlinear theory of hadrons, equivalent to the color singlet sector two dimensional QCD, is constructed. The phase space space of this theory is an infinite dimensional Grassmannian. The baryon number of QCD corresponds to a topological invariant (`virtual rank') of the Grassmannian. It is shown that the hadron theory has topological solitons corresponding to the baryons of QCD. $\frac{1}{N_c}$ plays the role of $\hslash$ in this theory; $N_c$ must be an integer for topological reasons. We also describe the quantization of a toy model with a finite dimensional Grassmannian as the phase space. In an appendix, we show that the usual Hartree--Fock theory of atomic and condensed matter physics has a natural formulation in terms of infinite dimensional Grassmannians.

59 pages

Cited by in corpus (33)

• Updating QCD${}_2$
• Two-dimensional QCD in the Coulomb gauge
• Partonic quasidistributions in two-dimensional QCD
• Closed formula for Wilson loops for $SU(N)$ Quantum Yang-Mills Theory in two dimensions
• Mesonic states and vacuum replicas in potential quark models for QCD
• A Lie Algebra for Closed Strings, Spin Chains and Gauge Theories
• Symplectic Manifolds, Coherent States and Semiclassical Approximation
• Boson Expansion Methods in (1+1)-dimensional Light-Front QCD
• Poisson Algebra of Wilson Loops and Derivations of Free Algebras
• A Model of Interacting Partons for Hadronic Structure Functions
• QCD(1+1) with massless quarks and gauge covariant Sugawara construction
• Covariant boost and structure functions of baryons in Gross-Neveu models
• Entropy of Operator-valued Random Variables: A Variational Principle for Large N Matrix Models
• A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit
• Nonconcentration of energy for a semilinear Skyrme model
• An Interacting Parton Model for Quark and Anti-quark distributions in the Baryon
• Large N limit of SO(N) scalar gauge theory
• Multi-matrix loop equations: algebraic & differential structures and an approximation based on deformation quantization
• Classical Mechanics and geometric Quantization on an Infinite Dimensional Disc and Grassmannian
• Parton Model from Bi-local Solitonic Picture of the Baryon in two-dimensions
• Supergrassmannian and large N limit of quantum field theory with bosons and fermions
• Large N limit of SO(N) gauge theory of fermions and bosons
• Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons
• Geometric Quantization on the Super-Disc
• A Lie-Algebraic Approach To the Kondo Problem
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models
• On two dimensional coupled bosons and fermions
• 2+1 Abelian `Gauge Theory' Inspired by Ideal Hydrodynamics
• On three dimensional coupled bosons
• On Baryon Number Non-Conservation in Two-Dimensional O(2N+1) QCD
• On lightest baryon and its excitations in large-N 1+1-dimensional QCD
• Modified Non-Euclidian Transformation on the SO(2N+2)/U(N+1) Grassmannian and SO(2N+1) Random Phase Approximation for Unified Description of Bose and Fermi Type Collective Excitations
• Self-Consistent-Field Method and $\tau$-Functional Method on Group Manifold in Soliton Theory: a Review and New Results