Titlebook: Geometry of the Fundamental Interactions; On Riemann‘s Legacy M. D. Maia Book 2011 Springer Science+Business Media, LLC 2011 Minkowski‘s s

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Symmetry,onal structure of nature [59]. However, the awareness of the importance of symmetry in physics became clear only after the debate on the negative result of the Michelson–Morley experiment and the subsequent interpretation of the relative motion between observers and observables given by Einstein. Th

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The Algebra of Observables,with the notions of physical space and of symmetry groups, the observables and the conditions of observations complete the basic elements of a physical theory..The observables themselves are usually invariant quantities in the sense that they can be measurable by different observers in different tim

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,Geometry of Space–Times,wing how the physics of space–time determines the geometry. In this, we were much influenced by Penrose’s writings and lectures [71]..As we have detailed in the introduction, we take the physical manifold as the space of perceptions in the sense of Kant. These perceptions are in one way or another a

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Scalar Fields,dinates are no longer enumerable. A simple but very intuitive example is given in [55, 82]..We emphasize what we have already said in Chapter 1: Point particles do not exist as a physically observable object, carrying mass, charge, momentum, spin, and other attributes in space–time. Regardless of th

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Vector, Tensor, and Spinor Fields,ysics, including the emergence of relativity and the relevance of the concept of symmetry in physics. Due to the importance of this combination of theoretical and experimental results to the development of gauge theory let us briefly review the basics of the electromagnetic field (for more details,