scholarly journals A Generalization of the Hopf Invariant

1946 ◽  
Vol 32 (6) ◽  
pp. 188-190 ◽  
Author(s):  
G. W. Whitehead
Keyword(s):  
Hopf Invariant

scholarly journals Dirac/Rarita–Schwinger plus Maxwell theories in ℝ × S3 spacetime in the Hopf coordinates

2020 ◽  
Vol 17 (13) ◽  
pp. 2050197
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev
Keyword(s):  
Maxwell Equations ◽  
Numerical Solutions ◽  
Separation Of Variables ◽  
Dirac Field ◽  
Hopf Invariant

We consider the sets of Dirac–Maxwell and Rarita–Schwinger–Maxwell equations in [Formula: see text] spacetime. Using the Hopf coordinates, we show that these equations allow separation of variables and obtain the corresponding analytic and numerical solutions. It is also demonstrated that the current of the Dirac field is related to the Hopf invariant on the [Formula: see text] fibration.

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