Papers › Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model
Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model
Gaoli Chen
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We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have s spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the 𝒪(1/N²) correction to the energy spectrum. A rough analysis shows that, when the bit number M is large, the ground state one-loop self-energy ΔE_G scale as M^(5-s/4) for even s and M^(4-s/4) for odd s. Particularly, in s=24, we have ΔE_G∼1/M, which resembles the Poincar\'e invariant relation P⁻∼1/P⁺ in (1+1) dimensions. We calculate analytically the one-loop correction for the ground energies with M=3 and s=1, 2. We then numerically confirm that the large M behavior holds for s≤4 cases.
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