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If we can apply dualism in the square of energy (there really are two kinds of energy: the potential and the kinetic), then

[tex] H^{+}=E^2 [/tex] this is a general form of kinetic energy.

[tex]H^{-}= - E^2 [/tex] this is a general form of potential energy.

then the square root of the general potential energy is a pure imaginary number.

[tex] \sqrt{H^{-}} = Ei [/tex]

H+ and H- is possible if and only if the infinitesimal forces and metrics are orthogonal.

If kinetic and potential energy are absolutely dual then

[tex] E_K E_P= E_K - E_P [/tex]

And the RHS expression can be defined as a Lagrangian.

[tex] H^{+}=E^2 [/tex] this is a general form of kinetic energy.

[tex]H^{-}= - E^2 [/tex] this is a general form of potential energy.

then the square root of the general potential energy is a pure imaginary number.

[tex] \sqrt{H^{-}} = Ei [/tex]

H+ and H- is possible if and only if the infinitesimal forces and metrics are orthogonal.

If kinetic and potential energy are absolutely dual then

[tex] E_K E_P= E_K - E_P [/tex]

And the RHS expression can be defined as a Lagrangian.

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