Chern-Simons theories are gauge theories defined in 2+1 dimensional space time [and more generally in any odd dimensional space-time], with many special features and applications. My interests are particularly concerned with their role in symmetry breaking, and the relation between the parity anomaly and the chiral anomaly, examples whereby classical symmetries are broken by quantum effects.
For a review see my Les Houches lectures [preprint version] from the 1998 Les Houches Summer School “TOPOLOGICAL ASPECTS OF LOW DIMENSIONAL SYSTEMS”; lectures published by Springer.
My book, Self-Dual Chern-Simons Theory, (Springer-Verlag, Heidelberg, 1995), reviews the existence, properties and applications of vortices and solitons in Chern-Simons systems
Some of my papers about Chern-Simons theories and their applications:
- “Topological (Chern-Simons) Quantum Mechanics”, G. V. Dunne, R. Jackiw, C.A. Trugenberger, published in Phys.Rev. D41 (1990) 661
- “Chern-Simons Theory in the Schrodinger Representation”, G. V. Dunne, R. Jackiw, C.A. Trugenberger, published in Annals Phys. 194 (1989) 197
- “Selfdual Chern-Simons solitons and two-dimensional nonlinear equations”, G. V. Dunne, R. Jackiw, S-Y. Pi, C.A. Trugenberger, published in Phys.Rev. D43 (1991) 1332
- “‘Peierls substitution’ and Chern-Simons quantum mechanics”, G. V. Dunne, R. Jackiw, published in Nucl.Phys.Proc.Suppl. 33C (1993) 114-118
- “Chern-Simons solitons, toda theories and the chiral model”, G. V. Dunne, published in Commun.Math.Phys. 150 (1992) 519-535
- “Odd Dimensional Gauge Theories And Current Algebra”, G. V. Dunne, C.A. Trugenberger, published in Annals Phys. 204 (1990) 281-314
- “Conformal symmetry and universal properties of quantum Hall states”, A. Cappelli, G. V. Dunne, C. A. Trugenberger, G. R. Zemba, published in Nucl.Phys. B398 (1993) 531-567 , arxiv preprint
- “Exact multi – anyon wave functions in a magnetic field”, G. V. Dunne, A. Lerda, S. Sciuto, C. A. Trugenberger, published in Nucl.Phys. B370 (1992) 601-635
- “On the finite temperature Chern-Simons coefficient”, G. V. Dunne, Ki-Myeong Lee, Chang-hai Lu, published in Phys.Rev.Lett. 78 (1997) 3434-3437 , arxiv preprint
- “Integer quantization of the Chern-Simons coefficient in a broken phase”, Lu-sheng Chen, G. V. Dunne, K. Haller, E. Lim-Lombridas, published in Phys.Lett. B348 (1995) 468-472 , arxiv preprint