Twisting all the way: from Classical Mechanics to Quantum Fields

Abstract

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative spacetime, i.e. we establish a noncommutative correspondence principle from *-Poisson brackets to *-commutators. In particular commutation relations among creation and annihilation operators are deduced.

32 pages. Added references and details in the introduction and in Section 5

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Cited by in corpus (73)

• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Noncommutative Gravity Solutions
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Noncommutative field theory with the Wick-Voros product
• Noncommutative field theory from angular twist
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• On second quantization on noncommutative spaces with twisted symmetries
• Dynamical symmetries in noncommutative theories
• Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Quantum statistics and noncommutative black holes
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Braided Cartan Calculi and Submanifold Algebras
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent
• A novel approach to non-commutative gauge theory
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Field Theory on Curved Noncommutative Spacetimes
• Differential forms and k-Minkowski spacetime from extended twist
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Duality and Braiding in Twisted Quantum Field Theory
• Noncommutative gravity with self-dual variables
• Involutive representations of coordinate algebras and quantum spaces
• Exponential Formulas and Lie Algebra Type Star Products
• Noncommutative correction to the entropy of charged BTZ black hole
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Noncommutative deformations of quantum field theories, locality, and causality
• Hopf Algebra Symmetry and String Theory
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• Wedge locality and asymptotic commutativity
• Twisted submanifolds of R^n
• Star Product Geometries
• Self-dual road to noncommutative gravity with twist: a new analysis
• Twist star products and Morita equivalence
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Voros product and the Pauli principle at low energies
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Braided Field Quantization from Quantum Poincare Covariance
• Noncommutative Conformal Field Theory in the Twist-deformed context
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Dirac Operators on Noncommutative Curved Spacetimes
• Twist Quantization of String and Hopf Algebraic Symmetry
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
• The Structure of Spacetime and Noncommutative Geometry
• QFT on homothetic Killing twist deformed curved spacetimes
• f-oscillators deformation for Moyal algebras
• Green's Functions for Translation Invariant Star Products
• Thermal effective potential in two- and three- dimensional non-commutative spaces
• Review of Twisted Poincare Symmetry
• Quantum Spacetimes from General Relativity?
• A bigravity model from noncommutative geometry
• Noncommutative spaces with twisted symmetries and second quantization