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| Jackiw–Rebbi model | |
|---|---|
| Name | Jackiw–Rebbi model |
| Introduced | 1976 |
| Creators | Roman Jackiw; Claudio Rebbi |
| Field | Theoretical physics; Quantum field theory; Condensed matter |
Jackiw–Rebbi model is a theoretical construction in relativistic quantum field theory that demonstrates how solitons, topological defects, and fermionic zero modes produce fractional quantum numbers. Developed by Roman Jackiw and Claudio Rebbi, the model illuminates connections between topology, anomalies, and spectral flow in one-dimensional systems and has influenced research in particle physics, condensed matter, and mathematical physics.
The Jackiw–Rebbi model arose in the context of studies by Roman Jackiw and Claudio Rebbi and built on prior work by Sidney Coleman, Gerard 't Hooft, Alexander Polyakov, and Kenneth Wilson on solitons and instantons. It formalizes interactions among Dirac fermions, scalar fields, and topological boundary conditions, connecting ideas from Julian Schwinger, Eugene Wigner, Lev Landau, and Murray Gell-Mann. The model provided a paradigm for charge fractionalization studied later by Robert Laughlin, Duncan Haldane, and Philip Anderson and informed approaches by Edward Witten, Gerard 't Hooft, and David Gross.
The original Jackiw–Rebbi setup couples a one-dimensional Dirac fermion to a scalar field with a kink profile, using techniques from Paul Dirac, Enrico Fermi, and Wolfgang Pauli for quantization and canonical commutation. Its Lagrangian density invokes Yukawa-type coupling analogous to Yukawa's meson theory and reflects symmetry-breaking patterns considered by Yoichiro Nambu, Jeffrey Goldstone, and Peter Higgs. The formulation uses the Dirac equation in one spatial dimension with boundary conditions influenced by work of John Bell, Roman Jackiw, and Claudio Rebbi and employs spectral analysis methods associated with Michael Berry, Simon Donaldson, and Isidore Singer.
Soliton solutions in the Jackiw–Rebbi model mirror classical solitons studied by Nikolay Bogolyubov, Lev Landau, and Vladimir Zakharov, while zero-energy fermion modes parallel phenomena in work by Felix Bloch, Lev Landau, and Philip Anderson. The zero mode emerges from index theorems related to Atiyah–Singer and Atiyah–Patodi–Singer and connects to spectral asymmetry concepts investigated by John von Neumann, Freeman Dyson, and Marcel Grossmann. Techniques from Richard Feynman, Murray Gell-Mann, and Julian Schwinger underpin the analysis of bound states and mode orthogonality.
Charge fractionalization in the Jackiw–Rebbi model is a consequence of topology and spectral flow described in papers by Jackiw, Rebbi, and collaborators and relates to the anomaly discussions by Stephen Adler, John Bell, and Roman Jackiw. Topological arguments draw on homotopy concepts formalized by Henri Poincaré, Henri Cartan, and Élie Cartan and invoke Chern–Simons ideas later developed by S. S. Chern, James Simons, and Edward Witten. Fractional quantum numbers influenced understanding in works by Robert Laughlin, Duncan Haldane, and Frank Wilczek and informed developments by Alexei Kitaev, Andreas Ludwig, and Xiao-Gang Wen.
Generalizations of the Jackiw–Rebbi model appear across condensed matter and high-energy physics, influencing research by Philip Anderson, Giorgio Parisi, and Carlo Rovelli. The model's concepts apply to polyacetylene theory by Alan Heeger, Alan MacDiarmid, and Hideki Shirakawa and to Majorana mode proposals by Ettore Majorana, Alexei Kitaev, and Frank Wilczek. Extensions intersect with conformal field theory work by Alexander Belavin, Alexander Zamolodchikov, and Paul Ginsparg and with supersymmetry research by Edward Witten, Pierre Ramond, and Julius Wess.
Experimental analogues inspired by the Jackiw–Rebbi model have been pursued in systems studied by Charles Kittel, Philip Anderson, and John Bardeen, and implemented in platforms championed by Saul Perlmutter, Alain Aspect, and Anton Zeilinger. Realizations include engineered domain walls in conducting polymers per Alan Heeger, solid-state heterostructures investigated by Leo Kouwenhoven, and cold-atom simulations advanced by Wolfgang Ketterle, Eric Cornell, and Carl Wieman. Observations draw on measurement techniques developed by Rainer Blatt, David Wineland, and Serge Haroche and inform proposals by Nadya Mason, Joel Moore, and Ashvin Vishwanath.
Category:Quantum field theory Category:Solitons Category:Condensed matter physics