Theories on noncommutative spaces and deformed symmetries

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.

Ph.D. thesis. Supervisor: Prof. Rabin Banerjee. Submitted on 07.07.2008 at Jadavpur University, Kolkata, India

References in corpus (70)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Field Theory and Lorentz Violation
• Gauge Theory on Noncommutative Spaces
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• A Gravity Theory on Noncommutative Spaces
• Non-Commutative Quantum Mechanics
• Quantum mechanics on the noncommutative plane and sphere
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Noncommutative Gravitational Quantum Well
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Non-commutative space-time of Doubly Special Relativity theories
• Deforming Einstein's Gravity
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Study of the neutron quantum states in the gravity field
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Noncommutative Standard Model: Model Building
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• Minimal Length Uncertainty Relation and gravitational quantum well
• Discrete Symmetries (C,P,T) in Noncommutative Field Theories
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Deformed Coordinate Spaces; Derivatives
• Comments on noncommutative gravity
• Noncommutative SO(n) and Sp(n) Gauge Theories
• Non-commutative Oscillators and the commutative limit
• Noncommutative Gravity
• Twisted Gauge Theories
• Renormalization of noncommutative U(N) gauge theories
• Second Order Noncommutative Corrections to Gravity
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• The noncommutative harmonic oscillator in more than one dimensions
• A note on the noncommutative correction to gravity
• UV-IR Mixing in Non-Commutative Plane
• String Geometry and the Noncommutative Torus
• Lie algebraic Noncommutative Gravity
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Hamiltonian Approach to Lagrangian Gauge Symmetries
• Unitary Quantum Physics with Time-Space Noncommutativity
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• The Free Particle in Deformed Special Relativity
• Remarks on the Noncommutative Gravitational Quantum Well
• Twist Symmetry and Gauge Invariance
• Snyder noncommutative space-time from two-time physics
• Representations of noncommutative quantum mechanics and symmetries
• Quantisation of $O(N)$ invariant nonlinear sigma model in the Batalin-Tyutin formalism
• Bosonisation and Duality Symmetry in the Soldering Formalism
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
• Duality Symmetries and Noncommutative Geometry of String Spacetime
• Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation
• Noncommutative gauge theories and Lorentz symmetry
• The Chiral Oscillator and its Applications in Quantum Theory
• Maps for currents and anomalies in noncommutative gauge theories
• Gauge Generators, Transformations and Identities on a Noncommutative Space
• Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
• Soldering Formalism: Theory and Applications
• Three lectures on noncommutative field theories
• Hamiltonian formulation of nonAbelian noncommutative gauge theories
• Covariantly Quantized Spinning Particle and its Possible Connection to Non-Commutative Space-Time
• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Twisted Space-Time Symmetry, Non-Commutativity and Particle Dynamics
• Noncommutative relativistic particle
• The Parametrized Relativistic Particle and the Snyder space-time
• Extended Space Duality in the Noncommutative Plane
• Constraint on Quantum Gravitational Well in Noncommutative Space