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Minimal Length Uncertainty Relation and Ultraviolet Regularisation

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arxiv hep-th/9612084 v1 pith:FUOSG75A submitted 1996-12-08 hep-th gr-qcmath-phmath.MPmath.QAq-algquant-ph

Minimal Length Uncertainty Relation and Ultraviolet Regularisation

classification hep-th gr-qcmath-phmath.MPmath.QAq-algquant-ph
keywords lengthregularisationtheoryultravioletdeltadetaildistancedistances
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Studies in string theory and quantum gravity suggest the existence of a finite lower limit $\Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example geometry is studied in detail.

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