Negative dimensions can be mathematically and physically meaningful.
Mathematical and physical frameworks, such as those in Lie group theory and the study of omnidimensional polytopes, demonstrate that negative dimensions can be formally defined and yield meaningful properties.
Papers [0] and [10] directly address the concept of negative dimensions, proving that they are mathematically sound extensions in Lie group theory and continuous geometry. The other papers are either tangential or deal with unrelated physical and mathematical topics.
Ruben L. Mkrtchyan, Alexander P. Veselov. On duality and negative dimensions in the theory of Lie groups and symmetric spaces. 2011. https://doi.org/10.1063/1.3625954
Demonstrates how symbolic formulas involving negative dimensions (such as U(-N)) naturally arise and extend within the theory of Lie groups and symmetric spaces.
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Szymon Łukaszyk. On the Omnidimensional Convex Polytopes and n-Balls in Negative, Fractional and Complex Dimensions. 2022. https://doi.org/10.20944/preprints202209.0089.v4
Proves that geometric formulas for volumes and surfaces of polytopes and n-balls remain continuous and meaningful in negative dimensions.
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