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- W4313447660 abstract "The generators of unitary representations of the Poincar'e group generate an algebra which maps smooth wavefunctions to smooth wavefunctions. This mathematical result is highly welcome to physicists, who previously just assumed their algebraic treatment of unbounded operators be justified. The smoothness, however, has the side effect that rough operators, which map smooth wavefunctions to functions which are not smooth, are inconsistent with Poincar'e symmetry: their product with the generators cannot be defined. Rough and smooth operators are not members of a common algebra. Transverse Heisenberg pairs $X^i$ and $P^j$, $i,jin {1,dots D-2}$, $P_z = P^{D-1}$, which commute with $P^+=(P^0 + P_z)/sqrt{2}$, as they occur in the light cone string, act roughly on massless multiplets. The domain of their algebra is not 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: in no dimension $D > 2$ does the light cone string admit a unitary representation of the Lorentz group. Massless multiplets are inconsistent with a spatial position operator $vec X$, which generates translations of the spatial momentum." @default.
- W4313447660 created "2023-01-06" @default.
- W4313447660 creator A5070900269 @default.
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- W4313447660 date "2022-12-30" @default.
- W4313447660 modified "2023-09-25" @default.
- W4313447660 title "The Rough with the Smooth of the Light Cone String" @default.
- W4313447660 doi "https://doi.org/10.48550/arxiv.2212.14822" @default.
- W4313447660 hasPublicationYear "2022" @default.
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