Position Space Interpretation for Generalized Parton Distributions
Position Space Interpretation for Generalized Parton Distributions
Position Space Interpretation for Generalized Parton Distributions
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use translational invariance to relate to same matrix element that<br />
appears in def. of <strong>for</strong>m factor<br />
〈 ρ(⃗r) ≡ ⃗R ∣ = ⃗0 ∣j 0 (⃗r) ∣R ⃗ 〉<br />
= ⃗0<br />
∫<br />
= |N |<br />
∫d 2 3 ⃗p d 3 ⃗p ′ 〈⃗p ′ |j 0 (⃗r) |⃗p〉<br />
∫<br />
= |N |<br />
∫d 2 3 ⃗p d 3 ⃗p ′ 〈⃗p ′ | j 0 (⃗0) |⃗p〉e i⃗r·(⃗p−⃗p′) ,<br />
∫ (<br />
= |N |<br />
∫d 2 3 ⃗p d 3 ⃗p ′ F − (⃗p ′ − ⃗p) 2) e i⃗r·(⃗p−⃗p′ )<br />
↩→ ρ(⃗r) =<br />
∫ d 3⃗ ∆<br />
(2π) 3 F(− ⃗∆ 2 )e i⃗r·⃗∆<br />
back<br />
<strong>Position</strong> <strong>Space</strong> <strong>Interpretation</strong> <strong>for</strong> <strong>Generalized</strong> <strong>Parton</strong> <strong>Distributions</strong> – p.33/55