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Quantum Gravitation String Theory:

Planck's Radius:
[tex]r_p = \sqrt{ \frac{ \hbar G}{ c^3}}[/tex]

Minimum observable length for a quantum string:
[tex]r_m = 2 \sqrt{ \alpha '}[/tex]

Planck's Radius is minimum observable length for a quantum string:
[tex]r_p = r_m[/tex]

Planck area of the hyperspace amplified Salam G* strong short range low energy gravity.
[tex]\sqrt{ \frac{ \hbar G}{ c^3}} = 2 \sqrt{ \alpha ^'}[/tex]

Alpha Prime:
[tex]\alpha ' = \frac{ \hbar G}{ 4 c^3}[/tex]
Alpha Prime is constant for a Planck Scale Bosonic String.

String Tension:
[tex]T_s = \frac{ 1}{2 \pi \alpha '}[/tex]

Quantum Gravitation String Tension:
[tex]T_g = \frac{ 2 c^3}{ \pi \hbar G}[/tex]

Relationship between distance and momentum:
[tex]\Delta L = \frac{ \hbar}{ p} + \alpha ' \frac{ p}{ \hbar}[/tex]

Quantum Gravitation distance and momentum:
[tex]\Delta L = \frac{ \hbar}{ p} + \frac{ G p}{4 c^3}[/tex]

Bosonic and fermionic hadronic Regge trajectory resonance:
[tex]J = \alpha ' E^2[/tex]
[tex]J = \frac{ \hbar G}{ 4 c^3} E^2[/tex]
[tex]E = \sqrt{ \frac{ 4 J c^3}{ \hbar G}}[/tex]

Reference:
http://superstringtheory.com/basics/basic3a.html
http://www.lepp.cornell.edu/spr/2001-05/msg0032717.html

 
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Nice summary of formulas. Your second formula is problematic because it means that in superstring theory there's a minimum distance that you can measure, the distance given by the formula. Alpha prime is also called Regge slope

Your fifth formula, the formula that you give for alpha prime is incorrect. Alpha prime is not a constant
 
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