scholarly journals Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

2018 ◽  
pp. 205-226
Author(s):  
Daniel Canarutto
Keyword(s):  
Dirac Fields ◽  
Lie Derivatives ◽  
Derivatives Of

Infinitesimal Deformations of ECD Fields

2020 ◽  
pp. 147-154
Author(s):  
Daniel Canarutto
Keyword(s):  
Lie Derivative ◽  
Dirac Fields ◽  
Lie Derivatives ◽  
Infinitesimal Deformations ◽  
Standard Notion ◽  
Derivatives Of

The standard notion of Lie derivative is extended in order to include Lie derivatives of spinors, soldering forms, spinor connections and spacetime connections. These extensions are all linked together, and provide a natural framework for discussing infinitesimal deformations of Einstein-Cartan-Dirac fields in the tetrad-affine setting.

scholarly journals Lie derivatives of sectorform fields

1988 ◽  
Vol 55 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Ivan Kolář
Keyword(s):  
Lie Derivatives ◽  
Derivatives Of

scholarly journals Spinor Lie derivatives and Fermion stress–energies

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150757
Author(s):  
A. D. Helfer
Keyword(s):  
Discrete Symmetries ◽  
Vector Fields ◽  
Lie Derivative ◽  
General Covariance ◽  
Arbitrary Vector ◽  
Lie Derivatives ◽  
Spinor Fields ◽  
Stress Energy ◽  
Derivatives Of ◽  
Apparent Conflict

Stress–energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here, I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld–van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress–energy. The differences in the definitions of spinors do not affect the results here, but could matter in certain quantum-gravity programs and for spinor transformations under discrete symmetries.

scholarly journals Mean-field sparse Jurdjevic–Quinn control

2017 ◽  
Vol 27 (07) ◽  
pp. 1223-1253 ◽  
Author(s):  
Marco Caponigro ◽  
Benedetto Piccoli ◽  
Francesco Rossi ◽  
Emmanuel Trélat
Keyword(s):  
Lyapunov Function ◽  
Control Function ◽  
Kinetic Equations ◽  
Mean Field ◽  
Transport Equations ◽  
Control Law ◽  
Time Varying ◽  
Nonlinear Transport ◽  
Lie Derivatives ◽  
Derivatives Of

We consider nonlinear transport equations with non-local velocity describing the time-evolution of a measure. Such equations often appear when considering the mean-field limit of finite-dimensional systems modeling collective dynamics. We address the problem of controlling these equations by means of a time-varying bounded control action localized on a time-varying control subset of small Lebesgue measure. We first define dissipativity for nonlinear transport equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, assuming that the uncontrolled system is dissipative, we provide an explicit construction of a control law steering the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function. In this sense the construction can be seen as an infinite-dimensional analogue of the well-known Jurdjevic–Quinn procedure. Moreover, the control law presents sparsity properties in the sense that the support of the control is small. Finally, we show that our result applies to a large class of kinetic equations modeling multi-agent dynamics.

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