Thirring model

Thirring model
Name	Thirring model
Field	Theoretical physics
Introduced	1958
Founder	Walter Thirring
Notable for	Exactly solvable interacting quantum field theory in (1+1) dimensions

Thirring model The Thirring model is an exactly solvable interacting quantum field theory in (1+1) dimensions notable for illustrating nontrivial features of renormalization, bosonization, and mass generation. It has influenced research across condensed matter and high-energy physics, connecting to integrable systems, conformal field theory, and many-body problems through exact techniques developed by leading figures in theoretical physics. The model serves as a testing ground for methods used by researchers associated with institutions such as CERN, Institute for Advanced Study, Princeton University, Harvard University, and University of Vienna.

Introduction

The Thirring model was introduced by Walter Thirring and became central to research pursued by theorists including Sin-Itiro Tomonaga, Julian Schwinger, Freeman Dyson, Kurt Symanzik, Paul Dirac, and Richard Feynman in the mid-20th century. It is studied alongside paradigmatic models such as the Ising model, Sine-Gordon model, Gross–Neveu model, Luttinger liquid, Kosterlitz–Thouless transition, and Heisenberg model by communities at Princeton, Harvard, MIT, Cambridge University, Oxford University, and ETH Zurich. Major developments involved contributions from researchers affiliated with CERN Theory Division, Max Planck Institute for Physics, Landau Institute for Theoretical Physics, and Steklov Institute of Mathematics.

Definition and Lagrangian

The model describes a self-interacting Dirac fermion in (1+1) dimensions defined originally by Walter Thirring and later analyzed by figures like Sin-Itiro Tomonaga and Julian Schwinger. Its Lagrangian density typically appears in textbooks used at Princeton University, Harvard University, University of Cambridge, ETH Zurich, and California Institute of Technology for illustrating interacting field theories. The standard form involves a kinetic Dirac term coupled to a current-current interaction, paralleling constructions considered by Paul Dirac and Wolfgang Pauli when exploring relativistic wave equations. This setup is often compared with models studied by Alexander Polyakov, Luis Alvarez-Gaumé, and Giovanni Montorsi in contexts linking gauge theories at CERN and condensed matter analogues investigated at Massachusetts Institute of Technology.

Exact Solutions and Bosonization

Exact solutions for the Thirring model were developed by researchers including Sidney Coleman, Stanley Mandelstam, Kenneth Wilson, Alexander Zamolodchikov, Ludwig Faddeev, and Evgeny Sklyanin. Bosonization techniques that relate fermionic descriptions to bosonic fields were elucidated by Jozef S. Bell, Jackiw, Roman Jackiw, Miguel Virasoro, and Gabriel Veneziano in settings overlapping with work at Harvard, Cambridge, and CERN. Connections to the Sine-Gordon model were clarified through mappings explored by Coleman and Mandelstam, while integrability aspects were pursued by Vladimir Drinfeld, Ludwig Faddeev, Alexander Zamolodchikov, and Boris Kupershmidt. Exact form factors and correlation functions were computed by groups linked to Institut des Hautes Études Scientifiques, Steklov Institute, and Max Planck Institutes.

Renormalization and Quantum Properties

Renormalization of the Thirring model was investigated using techniques advanced by Kenneth Wilson, Gerard 't Hooft, Wolfgang Pauli, Miguel Virasoro, and Kurt Symanzik. The model exhibits nontrivial anomalous dimensions and current algebra structures studied by J. Robert Schrieffer, Murray Gell-Mann, Robert Oppenheimer, Syed Qasim Zaidi, and Freeman Dyson. The exact renormalizability and scale dependence were clarified in works related to the renormalization group developed at Princeton University and Cornell University by leading theorists including Kenneth Wilson and Michael Fisher. Operator product expansions and conformal limits link the model to results by Alexander Polyakov, Alexander Zamolodchikov, Paul Ginsparg, and researchers at Yale University and University of Chicago.

Applications and Extensions

Applications span condensed matter and high-energy contexts explored at institutions such as Bell Labs, IBM Research, Los Alamos National Laboratory, Lawrence Berkeley National Laboratory, and Sandia National Laboratories. The Thirring model informs study of one-dimensional conductors like those examined in work by John Bardeen, Walter Brattain, and William Shockley and underpins theory for Luttinger liquids analyzed by F. Duncan M. Haldane, J. M. Luttinger, Robert Laughlin, and Philip Anderson. Extensions include massive and non-Abelian generalizations investigated by Gross–Neveu, Miguel Virasoro, Ludwig Faddeev, Edward Witten, and Gabriele Veneziano at Institute for Advanced Study and CERN. Numerical studies using methods developed by groups at Caltech, Stanford University, University of California, Berkeley, University of Illinois Urbana–Champaign, and ETH Zurich have applied lattice formulations and tensor network techniques pioneered by Steven White, Giuseppe Vidal, and Ian Affleck.

Historical Development and Key Results

Walter Thirring introduced the model in 1958, with seminal solutions and interpretations contributed by figures such as Sidney Coleman, Stanley Mandelstam, Kenneth Wilson, Alexander Zamolodchikov, Ludwig Faddeev, and Edward Witten. The model's exact solvability and bosonization duality were milestones comparable to breakthroughs by Enrico Fermi, Paul Dirac, Wolfgang Pauli, and Julian Schwinger in quantum field theory. Subsequent advances linking the Thirring model to integrable systems, conformal field theory, and condensed matter phenomena involved collaborations and research at CERN, Institute for Advanced Study, Max Planck Institute for Physics, Steklov Institute, and Landau Institute of Theoretical Physics. Key results include rigorous solutions for correlation functions, mappings to the Sine-Gordon model, identification of anomalous dimensions, and demonstrations of renormalizability that influenced later work by Gerard 't Hooft, Kenneth Wilson, Alexander Polyakov, and Edward Witten.

Category:Quantum field theory