Nambu–Jona-Lasinio model

Nambu–Jona-Lasinio model
Name	Nambu–Jona-Lasinio model
Field	Theoretical physics
Introduced	1961
Creators	Yoichiro Nambu; Giovanni Jona-Lasinio

Nambu–Jona-Lasinio model The Nambu–Jona-Lasinio model is a theoretical framework introduced in 1961 by Yoichiro Nambu and Giovanni Jona-Lasinio to describe spontaneous chiral symmetry breaking in interacting fermion systems, drawing analogies between particle physics and superconductivity. It has been influential across research by inspiring developments in quantum field theory, many-body physics, and effective descriptions of hadrons while interfacing with work by Richard Feynman, Murray Gell-Mann, and Julian Schwinger. The model underpins conceptual links to contemporary studies at CERN, Fermilab, DESY, and SLAC and informs computational efforts at institutions like the Max Planck Society and the Institute for Advanced Study.

Introduction

The origin of the model traces to Nambu's synthesis influenced by superconductivity concepts from John Bardeen, Leon Cooper, and Robert Schrieffer, and to Jona-Lasinio's field-theoretic formulation that resonated with developments by Werner Heisenberg, Paul Dirac, and Enrico Fermi. Early discussions connected with research directions pursued by Sin-Itiro Tomonaga, Julian Schwinger, Freeman Dyson, and Murray Gell-Mann, while subsequent analytical techniques were advanced by Kenneth Wilson, Steven Weinberg, and Gerard 't Hooft. The model has been central to pedagogical expositions by Richard Feynman, Abdus Salam, Sheldon Glashow, and Eugene Wigner, and it featured in seminars at Princeton University, Harvard University, and the University of Chicago alongside collaborations involving Isidor Rabi and Hans Bethe.

Formalism and Lagrangian

The canonical Lagrangian of the model is a four-fermion interaction inspired by work of Enrico Fermi and refined through formal approaches by Paul Dirac and Wolfgang Pauli, and the structure was clarified by contributions from Julian Schwinger and Freeman Dyson concerning propagators and Green's functions. Its formalism uses techniques developed by Kenneth Wilson in renormalization group analysis and by Gerard 't Hooft and Martinus Veltman in regularization, and it has been implemented in calculations at institutions such as CERN, Lawrence Berkeley National Laboratory, and the Rutherford Appleton Laboratory. Mathematical tools from John von Neumann, Norbert Wiener, and Paul Erdős underpin numerical treatments, while operator methods trace intellectual lineage to John von Neumann and Eugene Wigner.

Spontaneous Chiral Symmetry Breaking

Spontaneous chiral symmetry breaking within the model echoes conceptual frameworks advanced by Yoichiro Nambu and draws parallels to the BCS theory by John Bardeen, Leon Cooper, and Robert Schrieffer, and to Goldstone’s theorem formulated by Jeffrey Goldstone and elaborated by Jeffrey Goldstone, Abdus Salam, and Steven Weinberg. The generation of constituent masses reflects analytical work by Murray Gell-Mann and Francis Low and connects to anomalies studied by Stephen Adler and John Bell, with phenomenological implications examined at Brookhaven National Laboratory, the European Organization for Nuclear Research, and the Lawrence Livermore National Laboratory.

Extensions and Variants

Extensions of the model include the Polyakov–Nambu–Jona-Lasinio variant inspired by Alexander Polyakov and further developed in collaboration contexts involving Edward Witten, Sergei Novikov, and Andrei Sakharov, and gauge-coupled versions that relate to Yang–Mills theory introduced by Chen Ning Yang and Robert Mills. Lattice implementations echo computational strategies from Kenneth Wilson and Michael Creutz and have been pursued on supercomputing facilities at Los Alamos National Laboratory, Oak Ridge National Laboratory, and the National Institute for Computational Sciences. Supersymmetric adaptations connect conceptually to Pierre Ramond, Julius Wess, and Bruno Zumino, while finite-temperature generalizations relate to work by Lev Landau and Evgeny Lifshitz in statistical mechanics.

Applications in Hadron Physics

Applications to hadron spectroscopy and meson dynamics build on classification schemes by Murray Gell-Mann and Yuval Ne'eman and on current algebra techniques developed by Murray Gell-Mann, Steven Weinberg, and Benjamin Lee, with predictive use in analyses at SLAC, Fermilab, and KEK. The model informs constituent quark concepts championed by George Zweig and focuses on pseudoscalar and scalar mesons in ways that complement lattice QCD studies by Kenneth Wilson, David Gross, and Frank Wilczek, and experimental programs at J-PARC, Jefferson Lab, and the Relativistic Heavy Ion Collider led by researchers such as James Cronin and Miklos Gyulassy.

Renormalization and Regularization

Renormalization of the model invokes methods refined by Kenneth Wilson, Gerard 't Hooft, Martinus Veltman, and John Bell, and practical regularization schemes draw on Pauli–Villars techniques introduced by Wolfgang Pauli and Felix Villars and on dimensional regularization championed by Gerard 't Hooft and Steven Weinberg. Studies on nonrenormalizability and effective-field-theory perspectives align with approaches by Howard Georgi, Steven Weinberg, and Kurt Symanzik, with rigorous analyses referencing mathematical foundations by Laurent Schwartz and Israel Gelfand.

Relations to Other Models and Theories

The model is related to the BCS theory of superconductivity by John Bardeen, Leon Cooper, and Robert Schrieffer, to the Gross–Neveu model by David Gross and André Neveu, and to chiral perturbation theory developed by Jürg Gasser and Heinrich Leutwyler, while linking to quantum chromodynamics as formulated by Murray Gell-Mann and Harald Fritzsch and refined by David Gross, Frank Wilczek, and David Politzer. Connections extend to the Thirring model introduced by Walter Thirring, to Yukawa theory by Hideki Yukawa, and to effective Lagrangian approaches promoted by Steven Weinberg and Julius Wess, with implications for experimental programs at CERN, DESY, and Fermilab.

Category:Quantum field theory