We study a quantum version of the SU(2) Hopf fibration S7 → S4 and its associated twistor geometry. Our quantum sphere Sq7 arises as the unit sphere inside a q-deformed quaternion space Hq2. The resulting four-sphere Sq4 is a quantum analogue of the quaternionic projective space HP1. The quantum fibration is endowed with com- patible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space CPq3 and use it to study a system of anti-self-duality equations on Sq4, for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over Sq4

Differential and Twistor Geometry of the Quantum Hopf Fibration

LANDI, GIOVANNI
2012-01-01

Abstract

We study a quantum version of the SU(2) Hopf fibration S7 → S4 and its associated twistor geometry. Our quantum sphere Sq7 arises as the unit sphere inside a q-deformed quaternion space Hq2. The resulting four-sphere Sq4 is a quantum analogue of the quaternionic projective space HP1. The quantum fibration is endowed with com- patible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space CPq3 and use it to study a system of anti-self-duality equations on Sq4, for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over Sq4
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2601022
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