We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-Laplace-Beltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d'Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solutions. We also discuss the gauge freedom of the q-Maxwell field and give a q-spinor analysis of the q-field strength tensor.
Abstract. Associated to the standard SU q (n) R-matrices, we introduce quantum spheres S 2n−1 q , projective quantum spaces CP n−1 q , and quantum Grassmann manifolds G k (C n q ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziński and S. Majid [1].
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