Jona-Lasinio model

Jona-Lasinio model
Name	Jona-Lasinio model
Field	Theoretical Physics
Introduced	1961
Authors	Giovanni Jona-Lasinio
Related	Nambu–Jona-Lasinio model, Chiral symmetry, Spontaneous symmetry breaking

Jona-Lasinlio model.

Introduction

The Jona-Lasinio model is a quantum field theory framework introduced by Giovanni Jona-Lasinio building on ideas associated with Yoichiro Nambu and Miramontes? that illustrates dynamical spontaneous symmetry breaking in fermionic systems, connecting concepts from Julian Schwinger, Richard Feynman, Murray Gell-Mann, Tsung-Dao Lee, and Chen Ning Yang. It provides a tractable setting to study mass generation without invoking the Higgs boson mechanism, and influenced work by Gerard 't Hooft, Alexander Polyakov, Kenneth Wilson, Steven Weinberg, and François Englert. The model has cross-links to phenomena explored at CERN, Fermilab, SLAC National Accelerator Laboratory, Brookhaven National Laboratory, and in condensed matter contexts investigated by groups at Bell Labs and IBM Research.

Historical Development and Motivation

The model arose in the era of the early 1960s alongside research by Nambu–Jona-Lasinio model pioneers and contemporaries such as Yoichiro Nambu, Giovanni Jona-Lasinio, Murray Gell-Mann, S. L. Glashow, and Sheldon Glashow amid debates at institutions like Institute for Advanced Study, CERN, and Harvard University. Motivations tied to insights from experiments at Brookhaven National Laboratory, theoretical advances by Salam, Abdus, Steven Weinberg, and model building by Gerard 't Hooft and Martinus Veltman aimed to explain nucleon mass and chiral dynamics observed in CERN SPS and SLAC. Influential conferences including the Solvay Conference and workshops at Les Houches fostered exchanges with Paul Dirac, Enrico Fermi, and Lev Landau-era thinking.

Model Definition and Lagrangian

The core Lagrangian, formulated by Giovanni Jona-Lasinio with philosophical roots traceable to Yoichiro Nambu, features four-fermion contact interactions inspired by analogies to the BCS theory of superconductivity developed by John Bardeen, Leon Cooper, and Robert Schrieffer. The construction references algebraic methods from Richard Feynman path integrals, operator techniques used by Julian Schwinger, and canonical quantization approaches from Paul Dirac. The interaction terms respect global symmetries considered by Tsung-Dao Lee and Chen Ning Yang, and the model is often studied alongside renormalization insights from Kenneth Wilson and regularization schemes shaped by Gerard 't Hooft and Martinus Veltman.

Symmetry Breaking and Mass Generation

Spontaneous breaking of chiral symmetry in the model parallels mechanisms explored by Yoichiro Nambu and formalized later in the Higgs mechanism context by Peter Higgs, François Englert, and Robert Brout. Nambu–Goldstone modes analogous to those discussed by Jeffrey Goldstone and Yoichiro Nambu appear, and mass generation follows patterns comparable to analyses by Steven Weinberg and Gerard 't Hooft for gauge theories. The model illuminates how composite scalar states can emerge, a theme pursued at CERN and in studies by Sven Kullander and Ta-You Wu among others.

Renormalization and Regularization

Renormalization properties invoke techniques developed by Kenneth Wilson, Gerard 't Hooft, and Martin Veltman; the four-fermion interaction is nonrenormalizable in four dimensions following power-counting arguments attributed to Wolfgang Pauli-era formalisms and later expanded by Steven Weinberg. Regularization methods used include Pauli–Villars regulators introduced by Felix Villars and insights from dimensional regularization pioneered by Gerard 't Hooft and Martin Veltman, with conceptual connections to lattice regularization developed at CERN and by Kenneth Wilson at Brown University. Renormalization group flow inspired by Kenneth Wilson clarifies effective-field-theory treatments discussed in the literature of Edward Witten and David Gross.

Applications and Extensions

Applications span hadronic physics investigated by Murray Gell-Mann, Harald Fritzsch, and Heinrich Leutwyler; effective models for low-energy Quantum Chromodynamics studies performed at CERN and Jefferson Lab; condensed matter analogues explored by Philip Anderson and groups at Bell Labs; and extensions informing technicolor proposals by Steven Weinberg and S. Dimopoulos? in model-building at SLAC. The framework inspired work on inhomogeneous phases studied by Kurt Langfeld and Michael Thies, finite-temperature analyses relevant to Relativistic Heavy Ion Collider experiments at Brookhaven National Laboratory, and holographic approaches connected to research by Juan Maldacena and Edward Witten.

Mathematical Formalism and Solutions

Analytic techniques employ gap-equation derivations akin to mean-field theory used by John Bardeen and Leon Cooper; large-N expansion methods trace to work by Gerard 't Hooft and Edward Witten; and nonperturbative solutions utilize Schwinger–Dyson equations explored by Julian Schwinger and Freeman Dyson. Lattice implementations draw on numerical methods advanced at CERN and Fermilab and theoretical constructs related to integrable systems studied by Alexander Zamolodchikov and Ludwig Faddeev. The mathematical structure interfaces with functional integral formalism developed by Richard Feynman and operator algebra methods influenced by Paul Dirac.

Category:Quantum field theory