Theories on noncommutative spaces and deformed symmetries

2010/06/05 by Saurav Samanta, Samanta, Saurav
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Field (mathematics) #Gauge theory #Geometry #High Energy Physics - Theory (hep-th) #Homogeneous space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Philosophy #Physics #Pure mathematics #Space (punctuation) #Symmetry (geometry) #Theoretical physics #hep-th

paper · pdf · doi:10.48550/arxiv.1006.1039

published in arXiv (Cornell University) (Cornell University) · Ph.D. thesis. Supervisor: Prof. Rabin Banerjee. Submitted on 07.07.2008 at Jadavpur University, Kolkata, India

arxiv created 2010/06/05 · openalex publication_date 2010/06/05 · arxiv updated 2010/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external space time symmetries and the internal gauge symmetry in noncommutative theories are analyzed in detail.

Citations

• The Parametrized Relativistic Particle and the Snyder space-time
• Noncommutative relativistic particle
• Quantization of Gauge Systems
• Three lectures on noncommutative field theories
• Measurement of quantum states of neutrons in the Earth’s gravitational field
• Construction of gauge theories on curved noncommutative spacetime
• Twisted Space-Time Symmetry, Non-Commutativity and Particle Dynamics
• Noncommutative gauge theories and Lorentz symmetry
• Quantum states of neutrons in the Earth's gravitational field
• Twisted Gauge Theories
• Maps for currents and anomalies in noncommutative gauge theories
• On the principles of elementary quantum mechanics
• Representations of non-commutative quantum mechanics and symmetries
• Deformed conformal and super-Poincaré symmetries in the non- (anti-) commutative spaces
• String theory beyond the Planck scale
• Deforming Einstein's gravity
• Quantenmechanik und Gruppentheorie
• Twist symmetry and gauge invariance
• A gravity theory on noncommutative spaces
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Gauge theory on noncommutative spaces
• Quantum mechanics as a statistical theory
• Noncommutative quantum mechanics
• Noncommutative gravity

Related

• Introduction to noncommutative field and gauge theory
• Some Studies in Noncommutative Quantum Field Theories
• Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
• Noncommutative Gauge Theories and Gravity
• An Introduction to Noncommutative Spaces and their Geometry