scholarly journals On Noncommutative Geometry of the Standard Model: Fermion Multiplet as Internal Forms

2019 ◽  
pp. 69-82
Author(s):  
Ludwik Dąbrowski
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
Standard Model Fermion ◽  
The Standard Model

scholarly journals WHAT KIND OF NONCOMMUTATIVE GEOMETRY FOR QUANTUM GRAVITY?

2005 ◽  
Vol 20 (17n18) ◽  
pp. 1315-1326 ◽  
Author(s):  
PIERRE MARTINETTI
Keyword(s):  
Standard Model ◽  
Quantum Gravity ◽  
Noncommutative Geometry ◽  
Thermal Time ◽  
The Standard Model

We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.

scholarly journals Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
A. Bochniak ◽  
A. Sitarz ◽  
P. Zalecki
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Gauge Fields ◽  
Wick Rotation ◽  
Spectral Action ◽  
Geometry Model ◽  
The Standard Model ◽  
Cp Symmetry

Abstract We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological θ-terms for the electroweak gauge fields.

scholarly journals Correction to: The Standard Model in noncommutative geometry: fundamental fermions as internal forms

2019 ◽  
Vol 109 (11) ◽  
pp. 2585-2585
Author(s):  
Ludwik Dąbrowski ◽  
Francesco D’Andrea ◽  
Andrzej Sitarz
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
The Standard Model

scholarly journals Noncommutative geometry and the standard model vacuum

2006 ◽  
Vol 47 (5) ◽  
pp. 052305 ◽  
Author(s):  
John W. Barrett ◽  
Rachel A. Dawe Martins
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
The Standard Model

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.

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