Abstract
Symmetry simplifies the description of physical phenomena, in such a way that humans can understand them: the Latin word for “understanding,” capere, also means “to contain”; and as we are a part of it we cannot contain the full Universe, unless we find a way to reduce its complexity–this is the meaning of symmetry. Symmetry plays a particularly important role in particle physics, as it does in astrophysics and in cosmology. The key mathematical framework for symmetry is group theory: symmetry transformations form groups. Although the symmetries of a physical system are not sufficient to fully describe its behavior—for this purpose, one needs a complete dynamical theory—it is possible to use symmetry to discover fundamental properties of a system. Examples of symmetries include space–time symmetries, internal symmetries of particles, and the so-called gauge symmetries of field theories.
Symmetry simplifies the description of physical phenomena, in such a way that humans can understand them: the Latin word for “understanding,” capere, also means “to contain”; and as we are a part of it we cannot contain the full Universe, unless we find a way to reduce its complexity–this is the meaning of symmetry. Symmetry plays a particularly important role in particle physics, as it does in astrophysics and in cosmology. The key mathematical framework for symmetry is group theory: symmetry transformations form groups. Although the symmetries of a physical system are not sufficient to fully describe its behavior—for this purpose, one needs a complete dynamical theory—it is possible to use symmetry to discover fundamental properties of a system. Examples of symmetries include space–time symmetries, internal symmetries of particles, and the so-called gauge symmetries of field theories.
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Notes
- 1.
Emmy Noether (1882–1935) was a German mathematician. After dismissing her original plan to become a teacher in foreign languages, she studied mathematics at the University of Erlangen, where her father was a professor. After graduating in 1907, she worked for seven years as an unpaid assistant (at the time women could not apply for academic positions). In 1915, she joined the University of Göttingen, thanks to an invitation by David Hilbert and Felix Klein, but the faculty did not allow her to receive a salary, and she worked four years unpaid. In that time, she published her famous theorem. Finally, Noether moved to the USA to take up a college professorship in Philadelphia, where she died at the age of 53.
- 2.
Here, we are indeed cutting a long story short; we address the interested readers to a textbook in quantum physics to learn what is behind this fundamental point.
- 3.
Murray Gell-Mann (New York City 1929) entered the Yale university at the age of 15, and obtained his PhD from the MIT at 22. In the first part of his scientific career he gave important contributions to particle physics, in particular formulating the “quarks” hypothesis (the fanciful term was taken from Joyce’s novel Finnegans Wake). In a later stage he studied adaptive systems and emergent phenomena associated with complexity. He was awarded the Nobel Prize in Physics 1969 for his “discoveries concerning the classification of elementary particles and their interaction”.
- 4.
The Nobel Prize in Physics 1976 was awarded to Burton Richter (New York City 1931) and Samuel Ting (Ann Arbor, Michigan, 1936) “for their pioneering work in the discovery of a heavy elementary particle of a new kind”. Richter graduated from Far Rockaway High School, that also educated Richard Feynman; he became a professor at Stanford and later director of the Stanford Linear Accelerator Center. Ting was educated in China and Taiwan and returned to US for attending the University of Michigan, becoming later staff member of CERN and professor at the Massachusetts Institute of Technology (MIT). In the second part of his career Ting moved to astroparticle physics, and he is now the lead proposer and Principal Investigator of the AMS experiment (see Chap. 10). The Japanese K. Niu and collaborators had already published candidates for charm (no such name was ascribed to this new quark at that time) in a cosmic ray experiment using nuclear emulsions in 1971. These results, taken seriously in Japan, were not accepted as evidence for the discovery of charm by the majority of the US and European scientific communities. Once again, cosmic ray physics was the pathfinder.
- 5.
The problem of the determination of the quark masses is not trivial. We can define as a “current” quark mass the mass entering in the Lagrangian (or Hamiltonian) representation of a hadron; this comes out to be of the order of some MeV/\(c^2\) for u, d quarks, and \(\sim \)0.2 GeV/\(c^2\) for s quarks. However, the strong field surrounds the quarks in such a way that they acquire a “constituent ” (effective) mass including the equivalent of the color field; this comes out to be of the order of some 300 MeV/\(c^2\) for u, d quarks, and \(\sim \)0.5 GeV/\(c^2\) for s quarks. Current quark masses are almost the same as constituent quark mass for heavy quarks.
- 6.
Robert Hofstadter (1915–1990) was an American physicist. He was awarded the 1961 Nobel Prize in Physics “for his pioneering studies of electron scattering in atomic nuclei and for his consequent discoveries concerning the structure of nucleons.” He worked at Princeton before joining Stanford University, where he taught from 1950 to 1985. In 1948, Hofstadter patented the thallium activated NaI gamma-ray detector, still one of the most used radiation detectors. He coined the name “fermi,” symbol fm, for the scale of 10\(^{-15}\) m. During his last years, Hofstadter became interested in astrophysics and participated to the design of the EGRET gamma-ray space telescope (see Chap. 10).
- 7.
The Nobel Prize in Physics 1990 was assigned to Jerome I. Friedman, Henry W. Kendall, and Richard E. Taylor “for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics.”
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De Angelis, A., Pimenta, M. (2018). Particles and Symmetries. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-78181-5_5
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