Unitary Quantum Physics with Time-Space Noncommutativity

Abstract

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the commutative and noncommutative versions of the Hamiltonian have identical spectra.

18 pages, published version

References in corpus (12)

• The quantum structure of spacetime at the Planck scale and quantum fields
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Discrete Symmetries (C,P,T) in Noncommutative Field Theories
• Physical Instances of Noncommuting Coordinates
• Wave-Particle duality at the Planck scale: Freezing of neutrino oscillations
• Cosmological perturbations and short distance physics from Noncommutative Geometry
• Space-Time Noncommutativity, Discreteness of Time and Unitarity
• Non-Abelian Fluid Dynamics in Lagrangian Formulation
• Space-Time Noncommutativity from Particle Mechanics
• On Time-Space Noncommutativity for Transition Processes and Noncommutative Symmetries
• Noncommuting Gauge Fields as a Lagrange Fluid
• Troubles with Spacetime Noncommutative Theories: Tachyons or S-branes?

Cited by in corpus (43)

• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• UV-IR Mixing in Non-Commutative Plane
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Constraining non-commutative space-time from GW150914
• Generalized kappa-deformed spaces, star-products, and their realizations
• Noncommutative oscillator, symmetry and Landau problem
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Quantum Fields on the Groenewold-Moyal Plane
• Noncommutative Differential Forms on the kappa-deformed Space
• Space-Time Noncommutativity from Particle Mechanics
• Energy nonconservation as a link between $f(R,T)$ gravity and noncommutative quantum theory
• On Time-Space Noncommutativity for Transition Processes and Noncommutative Symmetries
• Particle-like solutions to classical noncommutative gauge theory
• Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Non-Hermitian quantum mechanics in non-commutative space
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Light Propagation in a Background Field for Time-Space Noncommutativity and Axionic Noncommutative QED
• Noncommutative configuration space. Classical and quantum mechanical aspects
• Noncommutativity and Reparametrisation symmetry
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• A New Limit for the Non-Commutative Space-Time Parameter
• Galilean symmetry in noncommutative Gravitational Quantum Well
• Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
• Cancellation of soft and collinear divergences in noncommutative QED
• Thermal Correlation Functions of Twisted Quantum Fields
• Canonical analysis of space-time noncommutative theories and gauge symmetries
• Using an intense laser beam in interaction with muon/electron beam to probe the Noncommutative QED
• Quantum Aspects of the Noncommutative Sine-Gordon Model
• The quantum sinh-Gordon model in noncommutative (1+1) dimensions
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Pinhole interference in three-dimensional fuzzy space
• Constraints, gauge symmetries, and noncommutative gravity in two dimensions
• Quantum Theory, Noncommutativity and Heuristics
• Waves on Noncommutative Spacetimes
• Theories on noncommutative spaces and deformed symmetries