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- W2138068004 abstract "Quantum field theory on Euclidean or Minkowski space is extremely successful. For suitably chosen action functionals one achieves a remarkable agreement of up to 10−11 between theoretical predictions and experimental data. However, combining the fundamental principles of both general relativity and quantum mechanics one concludes that space(-time) cannot be a differentiable manifold [1]. To the best of our knowledge, such a possibility was first discussed in [2]. To make this transparent, let us ask how we explore technically the geometry of space(-time). The building blocks of a manifold are the points labelled by coordinates {xμ} in a given chart. Points enter quantum field theory via the values of the fields at the point labelled by {xμ}. This observation provides a way to “visualise” the points: we have to prepare a distribution of matter which is sharply localised around {xμ}. For a perfect visualisation we need a δ-distribution of the matter field. This is physically not possible, but one would think that a δ-distribution could be arbitrarily well approximated. However, that is not the case, there are" @default.
- W2138068004 created "2016-06-24" @default.
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- W2138068004 date "2004-07-01" @default.
- W2138068004 modified "2023-09-27" @default.
- W2138068004 title "RENORMALISATION OF NONCOMMUTATIVE SCALAR FIELD THEORIES" @default.
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- W2138068004 doi "https://doi.org/10.1142/9789812702562_0006" @default.
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