2022/03/06 by Norbert Dragon, Dragon, Norbert, Florian Oppermann +1
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2203.03063
If the algebra of the Poincaré generators is enlarged by the spacetime position operator X=(X0,…, XD-1) then the spectra of the momentum P and the mass P2 are unbounded and continuous. In particular, the constraint (P2 - m2)Ψphys=0 of the covariant string has no solution in the space which admits X: All physical states vanish, Ψphys=0. Vice versa, a space spanned by mass eigenstates does not admit the position operator X in D dimensions. A massless particle does not allow a spatial position operator X. The domain of Heisenberg pairs Xi and Pj, i,j∈ \1,… D-2\, D > 2, which commute with P+=(P0 + Pz)/√(2), [P+,Xi] = 0, does not allow for a space with massless or tachyonic states, which is mapped to itself by rotations, leave alone Lorentz transformations. This is true in all dimensions and makes the algebraic calculation of the critical dimension, D=26, of the bosonic string meaningless: the light cone string is not Lorentz invariant.