Lattice QCD${}_2$ effective action with Bogoliubov transformations

Abstract

In the Wilson's lattice formulation of QCD, a fermionic Fock space of states can be explicitly built at each time slice using canonical creation and annihilation operators. The partition function $Z$ is then represented as the trace of the transfer matrix, and its usual functional representation as a path integral of $\exp (-S)$ can be recovered in a standard way. However, applying a Bogoliubov transformation on the canonical operators before passing to the functional formalism, we can isolate a vacuum contribution in the resulting action which depends only on the parameters of the transformation and fixes them via a variational principle. Then, inserting in the trace defining $Z$ an operator projecting on the mesons subspace at each time slice and making the physical assumption that the true partition function is well approximate by the projected one, we can also write an effective quadratic action for mesons. We tested the method in the renowned 't Hooft model, namely QCD in two spacetime dimensions for large number of colours, in Coulomb gauge.

8 pages, 1 figure. Proceedings of XIII Quark Confinement and the Hadron Spectrum - Confinement2018, 31 July - 6 August 2018, Maynooth University, Ireland

References in corpus (5)

• Composite boson dominance in relativistic field theories
• A semi-variational approach to QCD at finite temperature and baryon density
• Bogoliubov transformations and fermion condensates in lattice field theories
• Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential
• Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD