Ultraviolet Finite Quantum Field Theory on Quantum Spacetime

  title={Ultraviolet Finite Quantum Field Theory on Quantum Spacetime},
  author={Dorothea Bahns and Sergio Doplicher and Klaus Fredenhagen and Gherardo Piacitelli},
  journal={Communications in Mathematical Physics},
Abstract: We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates qj−qk are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation… 

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject

On second quantization on noncommutative spaces with twisted symmetries

By the application of the general twist-induced ⋆-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime into a noncommutative language. The


The understanding of fundamental interactions is based on the concept of quantum field theory in combination with gauge fields. It represents a unification of the theory of special relativity and

Spectral Regularization and its Applications in Quantum Field Theory

The argument of this thesis is the ultraviolet Spectral Regularization of Quantum Field Theory (QFT). We describe its genesis, its definition and apply it to physically interesting models. One of the

Born--Oppenheimer decomposition for quantum fields on quantum spacetimes

Quantum Field Theory on Curved Spacetime (QFT on CS) is a well established theoretical framework which intuitively should be a an extremely effective description of the quantum nature of matter when

A ug 2 00 6 Quantum Field Theory on Quantum Spacetime

Condensed account of the Lectures delivered at the Meeting on Noncommutative Geometry in Field and String Theory, Corfu, September 18 20, 2005. Introduction. Can Quantum Mechanics and General

Dirac Field on Moyal-Minkowski Spacetime and Non-commutative Potential Scattering

The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts

Minimal length in quantum space and integrations of the line element in Noncommutative Geometry

We question the emergence of a minimal length in quantum spacetime, comparing two notions that appeared at various points in the literature: on the one side, the quantum length as the spectrum of an

Quantum field theory and composite fermions in the fractional quantum Hall effect

We derive a composite fermion model for the fractional quantum Hall effect from relativistic quantum electrodynamics. With simple arguments it is shown that a special Chern Simons transformation of



Space/time non-commutative field theories and causality

Abstract. As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naïve path integral Feynman rules. One of the proposals is to use the

Noncommutative geometry and the standard model of elementary particle physics

Foundations of Noncommutative Geometry and Basic Model Building.- Spectral Triples and Abstract Yang-Mills Functional.- Real Spectral Triples and Charge Conjugation.- The Commutative Case: Spinors,

Field Theory on Noncommutative Space-Time and the Deformed Virasoro Algebra

We consider a field theoretical model on the noncommutative cylinder which leads to a discrete-time evolution. Its Euclidean version is shown to be equivalent to a model on the complex $q$-plane. We

Divergencies in a field theory on quantum space

The S Matrix in Quantum Electrodynamics

The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering

D-branes and Deformation Quantization

In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract


The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (Euclidean) time parameter. In agreement with the general idea of

Introduction to the theory of quantized fields

This site is also available in the following languages: Български Català Deutsch Ελληνικά English Español Français Hrvatski Italiano Norsk/Bokmål Polski Português Русский Slovensky Svenska ( ) ( )

Space-time noncommutative field theories and unitarity