scholarly journals On the Gauss-Bonnet for the quasi-Dirac operators on the sphere

2017 ◽  
Vol 50 (1) ◽  
pp. 66-71
Author(s):  
Andrzej Sitarz
Keyword(s):  
Scalar Curvature ◽  
Dirac Operators ◽  
Two Dimensional ◽  
Spectral Triples ◽  
Bonnet Theorem

Abstract We investigate examples of Gauss-Bonnet theorem and the scalar curvature for the two-dimensional commutative sphere with quasi-spectral triples obtained by modifying the order-one condition.

scholarly journals Dirac operators and spectral triples for some fractal sets built on curves

2008 ◽  
Vol 217 (1) ◽  
pp. 42-78 ◽  
Author(s):  
Erik Christensen ◽  
Cristina Ivan ◽  
Michel L. Lapidus
Keyword(s):  
Dirac Operators ◽  
Spectral Triples ◽  
Fractal Sets

scholarly journals Renormalizable Gravitational Action That Reduces to General Relativity on the Mass-Shell

Galaxies ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 81
Author(s):  
Peter Morley
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Standard Model ◽  
Scalar Curvature ◽  
Gravitational Constant ◽  
Mass Shell ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Gravitational Action ◽  
The Standard Model

We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement. Implications of this equation are discussed in the paper. In particular, we show (in the last section) that this equation is the transformation that relates four-dimensional physics to two-dimensional physics.

A Continuum Approach to 2D-Quantum Gravity for c>1

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3247-3279
Author(s):  
M. Martellini ◽  
M. Spreafico ◽  
K. Yoshida
Keyword(s):  
Quantum Gravity ◽  
Scalar Curvature ◽  
Free Parameter ◽  
Central Charge ◽  
Flat Space ◽  
String Tension ◽  
Physical Significance ◽  
Two Dimensional ◽  
Continuum Approach ◽  
Gauge Fixing

Two dimensional induced quantum gravity with matter central charge c>1 is studied by carefully treating both diffeomorphism and Weyl symmetries. It is shown that, for the gauge fixing condition R(g) (scalar curvature) = const, one obtains a modification of the David–Distler–Kawai version of KPZ scaling. We obtain a class of models with real string tension for all values c>1. They contain a free parameter which is, however, strongly constrained by the requirement of the non triviality of the model. The possible physical significance of the new model is discussed. In particular we note that it describes smooth surfaces imbedded in d-dimensional flat space time for arbitrary d, which is consistent with recent numerical results for d=3.

Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
E. M. Solouma ◽  
M. M. Wageeda
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Two Dimensional

AbstractIn this paper we analyzed the problem of studying locally the scalar curvature

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