Possible Equations For Vector Bundles

 Here is something that I mathematically derived, as to what the Potential mathematical expressions for the Hamiltonian-Related Reductional Non Abelian/Abelian Vector Bundles are to be, for cotangent bundle R(N).  This is when one is to consider, that the energy of a cohesive set of discrete energy quanta, is in this particular case, to act as the directly associated Hamiltonian Operator (as the overall energy of the system); and, if one is to consider "D," to work to represent the number of overall proximal local spatial dimensions, that are here to be present for the inferred Hamiltonian Operator, -- to where, "D" = "N."

Hamiltonian-Related Reductional Non Abelian Vector Bundle:

[[[The Real Riemann-Related component of the Force of the directly associated Hamiltonian Operator] - 

[The Imaginary component of the Force of the directly associated Hamiltonian Operator]] + 

[(The directly corresponding Hamiltonian Operator)/(2*PI*D)]] -- (as taken, via a correlative set of directorals). 

Hamiltonian-Related Reductional Abelian Vector Bundle:

[[[The Real Riemann-Related component of the Force of the directly associated Hamiltonian Operator] -

[The Imaginary component of the Force of the directly associated Hamiltonian Operator] -

[(i*(The directly corresponding Hamiltonian Operator))/(2*PI*D)]] -- (as taken, via a correlative set of directorals).

(P.S.: -- To those who are not much familiar with math, "i" = (The square root of (-1).))

Please tell me if these equations make an adequate amount of sense, since I have just recently derived this set of mathematical expressions! (P.S.: Dialogue works to indicate that NO ONE is perfect, -- and we can ALL learn from each other!) To Be Continued! Sincerely, SAMUEL DAVID ROACH. (1989).