Field Theory on a q = −1 Quantum Plane
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We build a q = −1 deformation of a plane on a product of two copies of algebras of functions on the plane. This algebra contains a subalgebra of functions on the plane. We present a general scheme (which could be also used to construct a quaternion from pairs of complex numbers) and we use it to derive differential structures and metrics, and discuss sample field-theoretical models.
Keywordsquantum plane noncommutative geometry
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