scholarly journals Unified prescription for the generation of electroweak and gravitational gauge field Lagrangian on a principal fiber bundle

1990 ◽  
Vol 31 (12) ◽  
pp. 3047-3052 ◽  
Author(s):  
Theo Verwimp
Keyword(s):  
Gauge Field ◽  
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.

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.

The composition equipment for congruence of hypercentred planes

2019 ◽  
pp. 61-67
Author(s):  
A. V. Vyalova
Keyword(s):  
Projective Space ◽  
Fundamental Group ◽  
Fiber Bundle ◽  
Principal Bundle ◽  
First Order ◽  
Principal Fiber Bundle ◽  
Dimensional Plane ◽  
Fundamental Object ◽  
Dimensional Projective Space

In n-dimensional projective space Pn a manifold Vnm , i. e., a congruence of hypercentered planes Pm , is considered. By a hypercentered planе Pm we mean m-dimensional plane with a (m – 1)-dimensional hyperplane Lm1 , distinguished in it. The first-order fundamental object  of the congruence is a pseudotensor. The principal fiber bundle Gr (Vnm) is associated with the congruence, r  n(n m1)  m2. . The base of the bundle is the manifold Vnm and a typical fiber is the stationarity subgroup Gr of a centered plane Pm . In principal fiber bundle a fundamental-group connection is given using the field of the object Г . The composition equipment for the congruence is set by means of a point lying in the plane and not belonging to its hypercenter and an (n – m – 1)-dimensional plane, which does not have common points with the hypercentered plane. The composition equipment is given by field of quasitensor  . It is proved that the composition equipment for the congruence Vnm of hypercentred m-planes Pm induces a fundamental-group connection with object Г in the principal bundle Gr (Vnm ) associated with the congruence. In proof, the envelopments Г  Г(, ) are built for the components of the connection object Г .

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