Abstract
During the last century it was more and more recognized that fundamental physics can be based on symmetries. In this introductory chapter the notion of symmetry in terms of operations and invariants is brought to mind. Further it is explained that in this book “fundamental physics” is understood in the sense of “elementary particle theory and relativity theories”, and that the symmetry operations dealt with act on the level of the action as variational symmetries. Further topics are different versions of symmetries, the benefit of symmetries, and an overview of the essential symmetry groups as they show up in various fields ranging from classical physics to particle physics and theories of gravitation.
Symmetry, as wide or as narrow you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
Hermann Weyl in his reflections about symmetry [552].
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Notes
- 1.
This is a slogan attributed to C.S.Yang, which I was not able to find. It is stated in [247]. Interestingly enough many people jumped on it, as one can track in looking for this slogan in an Internet search machine.
- 2.
This is cited at many places, for instance in [57] without mentioning the source.
- 3.
The term ‘dynamic’ is by some used in the sense of what is called in this book ‘Lie symmetries’, by others in the sense of ‘local symmetries’.
- 4.
My “so called” refers to “theory”, since–although undoubtably highly developed–the string picture is still on the level of a possible model of nature.
- 5.
I do not expect the reader to understand this jargon here in the introduction, but I promise that the catchwords ‘de Sitter’ and ‘conformal’ will be explained later. Some more words will be spent on this “gravity/gauge theory conjecture” in Sect. 8.4.
- 6.
No joke: It the army I was told that there are three laws.
- 7.
named after Ernst Florens Friedrich Chladni (German 1756–1827), who in the encyclopedias is called either a German, a Hungarian, or a Slovak. From this confusion you may realize how unstable–and perhaps unimportant–the status of nationality was at his times.
- 8.
It is not in the scope of this book to derive these solutions. You either believe me or cheque it yourself...
- 9.
Strictly speaking the following applies to Hamilton’s function \(\bar{S}\) which relates to the action as \(S = \bar{S}(t_2)\)-\(\bar{S}(t_1)\); see Sect. 2.1.4
- 10.
The definitions of invariance and covariance and their mutual relation are not really obvious, and depend on the dynamical and the background structure. More about this in Sect. 7.5.3.
- 11.
The quantitative relation is \(m_n = 1.00135 m_p\).
- 12.
Observe that the word “dictates” shows up in many of the quotes of Sect. 1.1.
- 13.
\(\ldots \,\)and maybe a quest of renormalizability.
- 14.
Also to be found in the Stanford Encyclopedia of Philosophy; http://plato.stanford.edu/entries/symmetry-breaking/.
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Sundermeyer, K. (2014). Introduction. In: Symmetries in Fundamental Physics. Fundamental Theories of Physics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-06581-6_1
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