scholarly journals Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

2015 ◽  
Author(s):  
Paul Benioff
Keyword(s):  
Gauge Theory ◽  
Fiber Bundle ◽  
Principal Fiber Bundle

Topological invariance of the Hall conductance and quantization

2015 ◽  
Vol 29 (24) ◽  
pp. 1550135
Author(s):  
Paul Bracken
Keyword(s):  
Chern Class ◽  
Fiber Bundle ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Hall Conductance ◽  
Integer Multiple ◽  
Principal Fiber Bundle ◽  
Topological Invariance ◽  
First Chern Class

It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a [Formula: see text] principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of [Formula: see text]. The formalism can be extended to deduce the fractional conductivity as well.

FIVE-DIMENSIONAL CHERN–SIMONS GRAVITY WITH NONLINEAR ELECTRODYNAMICS

2001 ◽  
Vol 16 (38) ◽  
pp. 2421-2429 ◽  
Author(s):  
ALFREDO MACÍAS ◽  
ENRIQUE LOZANO
Keyword(s):  
Gauge Theory ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Fiber Bundle ◽  
Reduction Process ◽  
Nonlinear Electrodynamics ◽  
Dimensional Theory ◽  
Chern Simons ◽  
Bonnet Term ◽  
Bundle Structure

We consider five-dimensional theory of gravity proposed recently by Chamseddine. It is based on the Chern–Simons five-form and the SO(1,5) gauge group. The action naturally contains a Gauss–Bonnet term, an Einstein term and a cosmological constant. We shall see that by imposing to this action the five-dimensional principal fiber bundle structure and the toroidal dimensional reduction process, the resulting U(1) gauge theory contains non-minimal couplings to gravity and nonlinear modifications to the standard Einstein–Maxwell–dilaton theory.

scholarly journals Connections from trivializations

2016 ◽  
Vol 70 (2) ◽  
pp. 83
Author(s):  
Jan Kurek ◽  
Włodzimierz Mikulski
Keyword(s):  
Fiber Bundle ◽  
Structural Group ◽  
Natural Operator ◽  
Principal Fiber Bundle ◽  
Linear Connections ◽  
Torsion Free ◽  
Natural Operators

Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.

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