Letters in Mathematical Physics

, Volume 79, Issue 1, pp 75–94 | Cite as

Cauchy Problem for the Fermion Field Equation Coupled With the Chern–Simons Gauge



We study initial value problems of the Chern–Simons–Dirac equations. With the Lorentz gauge condition they are formulated in the second-order hyperbolic equations. Under the Coulomb gauge condition Dirac equation is coupled with the elliptic equations which show some smoothing properties of the gauge field. With the temporal gauge condition divergence-curl decomposition and elliptic estimates will be used.


Chern–Simons–Dirac Strichartz null form elliptic div-curl decomposition 

Mathematics Subject Classification (2000)

35L15 35L45 35Q40 35F25 


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© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan

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