The Riemann hypothesis and tachyonic off-shell string scattering amplitudes


Abstract:

The study of the 4-tachyon off-shell string scattering amplitude A4(s, t, u) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “spins” J. The latter J belong to the Regge trajectories in the t, u channels which are defined by -J(t)=-1-12t=β(t)=12+iλ; -J(u)=-1-12u=γ(u)=12-iλ, with λ= real. These values of β(t) , γ(u) given by 12±iλ, respectively, coincide precisely with the location of the critical line of nontrivial Riemann zeta zeros ζ(zn=12±iλn)=0. It is argued that despite assigning angular momentum (spin) values J to the off-shell mass values of the external off-shell tachyons along their Regge trajectories is not physically meaningful, their net zero-spin value J(k1) + J(k2) = J(k3) + J(k4) = 0 is physically meaningful because the on-shell tachyon exchanged in the s-channel has a physically well defined zero-spin. We proceed to prove that if there were nontrivial zeta zeros (violating the Riemann Hypothesis) outside the critical line Realz=1/2 (but inside the critical strip) these putative zeros don′t correspond to any poles of the 4-tachyon off-shell string scattering amplitude A4(s, t, u). We finalize with some concluding remarks on the zeros of sinh(z) given by z= 0 + i2 πn, continuous spins, non-commutative geometry and other relevant topics.

Año de publicación:

2022

Keywords:

    Fuente:

    scopusscopus

    Tipo de documento:

    Article

    Estado:

    Acceso abierto

    Áreas de conocimiento:

    • Optimización matemática

    Áreas temáticas de Dewey:

    • Matemáticas
    • Física
    Procesado con IAProcesado con IA

    Objetivos de Desarrollo Sostenible:

    • ODS 9: Industria, innovación e infraestructura
    • ODS 17: Alianzas para lograr los objetivos
    • ODS 4: Educación de calidad
    Procesado con IAProcesado con IA

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