Noncommutative geometry and quantum field theory

2005 ◽  
pp. 213-221 ◽  
Author(s):  
Petr P. Kulish
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Noncommutative Geometry ◽  
Quantum Field

scholarly journals Finite quantum field theory in noncommutative geometry

1996 ◽  
Vol 35 (2) ◽  
pp. 231-244 ◽  
Author(s):  
H. Grosse ◽  
C. Klimčík ◽  
P. Prešnajder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Noncommutative Geometry ◽  
Quantum Field

scholarly journals Macroscopic traversable wormholes with zero tidal forces inspired by noncommutative geometry

2015 ◽  
Vol 24 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Peter K. F. Kuhfittig
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Energy Density ◽  
Noncommutative Geometry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Quantum Field ◽  
Tidal Forces ◽  
Traversable Wormholes ◽  
Asymptotic Flatness

This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum-field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies the usual requirements, including asymptotic flatness.

QUANTIZING FIELD THEORIES IN NONCOMMUTATIVE GEOMETRY AND THE AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2355-2358 ◽  
Author(s):  
KAMRAN KAVIANI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Noncommutative Geometry ◽  
Field Theories ◽  
Quantum Field ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory

By using the approach of noncommutative geometry, we study spinors and scalars on the two layers AdSd+1 space. We have found that in the boundary of two layers AdSd+1 Space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of noncommutative geometry.

scholarly journals Unification of gravity and quantum field theory from extended noncommutative geometry

2017 ◽  
Vol 32 (05) ◽  
pp. 1750030 ◽  
Author(s):  
Hefu Yu ◽  
Bo-Qiang Ma
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Gravity Field ◽  
Noncommutative Geometry ◽  
Coordinate Frame ◽  
Quantum Field ◽  
Gravity Effect ◽  
Frame Bundle ◽  
The Standard Model

We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.

INTRODUCTION TO BRAIDED QUANTUM FIELD THEORY

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2461-2466 ◽  
Author(s):  
ROBERT OECKL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Group ◽  
Noncommutative Geometry ◽  
Quantum Groups ◽  
Symmetry Groups ◽  
Quantum Field ◽  
Noncommutative Spaces ◽  
Small Scales ◽  
Group Symmetries

Indications from various areas of physics point to the possibility that space-time at small scales might not have the structure of a manifold. Noncommutative geometry provides an attractive framework for a perhaps more accurate description of nature. It encompasses the generalisation of spaces to noncommutative spaces and of symmetry groups to quantum groups. This motivates efforts to extend quantum field theory to noncommutative spaces and quantum group symmetries. One also expects that divergences of conventional theories might be regularised in this way.

Noncommutative Geometry and Quantum Field Theory

2005 ◽  
pp. 2705-2760 ◽  
Author(s):  
Sergio Doplicher ◽  
Mario Paschke ◽  
Rainer Verch ◽  
Eberhard Zeidler
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Noncommutative Geometry ◽  
Quantum Field
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