By Veltman M.J.G.
This lecture is set my contribution to the facts of renormalizability of gauge theories. there's after all no completely transparent separation among my contributions and people of my co-laureate 't Hooft, yet i'll restrict myself to a couple short reviews on these guides that hold merely his identify. an intensive overview at the topic together with extra exact references to modern paintings are available in other places (Veltman, 1992a).
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Additional info for Nobel lecture: from weak interactions to gravitation
The connection, which represents the gravitation potential, relates the features on various tangent spaces to present a global order. The logic of the local symmetries in general relativity and its similarity to gauge field theories are most apparent in the fiber bundle formulation (Appendix B). The equivalence principle has many formulations. A weak form of the principle is the equivalence of inertial and gravitational masses. Einstein's original version focuses on how the effects of a homogeneous gravitational field can be canceled by a nonrotating uniformly accelerating reference frame.
It is characteristic of scientific theories that their contents are specific and their predictions pinpoint as to be easily verified or falsified by experiments. The specificity of physical theories is their strength; it also limits their liability. The philosophical motivation for developing a physical theory is distinct from and irrelevant to the content of the theory. General relativity and hidden variables are examples of theories driven by a realistic outlook, yet their topics are certain physical properties, not realism.
Cartesian geometry forces us to invoke points and lines as a package. Also, it applies only to a special kind of spaces that are coverable by a single coordinate system. These requirements are too stringent for the theory of general relativity. Differential Geometry^ The first breakthrough in geometry occurred with Carl Friedrich Gauss's theory of surfaces, where the grid of parallel lines is replaced by an arbitrary dense grid of ordered curves. The curves are not equally spaced; Gauss's important idea is that the spacing between them is not a consideration at all.