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Can anyone provide me with a rigorous mathematical definition of the fundamental particles (all fundamental bosons and fermions), reflecting the analogy of action of groups with interaction of particles, isospin and mediating forces? An answer would be preferable, but a link of an appropriate source would also suffice.

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Would this help you better define what you're looking for? en.wikipedia.org/wiki/Wightman_axioms –  Danu Apr 19 at 16:29
    
Related: physics.stackexchange.com/q/27665/2451 and links therein. –  Qmechanic Apr 19 at 17:22
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@Danu I understand the 6/7 Wightman axioms but fail to capture how does the concepts of fundamnetal particles, quarks-leptons, or bosons mediating forces etc. come from those. –  smiley06 Apr 19 at 18:11
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Actually, the book The Structure and Interpretation of the Standard Model addresses this very question! –  Alex Nelson Apr 19 at 19:31
    
Perhaps this paper could be a starting point, I didn't read it by now but it seems to deal with a very related question and tries to restrict itself to first quantization to avoid some mathematical pittfalls...: philsci-archive.pitt.edu/1626 –  student Apr 19 at 19:34

1 Answer 1

The standard model of particle physics is a theoretical framework that encapsulates almost all elementary particle data to date. The full Lagrangian takes pages.

In your comment:

@Danu I understand the 6/7 Wightman axioms but fail to capture how does the concepts of fundamnetal particles, quarks-leptons, or bosons mediating forces etc. come from those.

Physics theoretical models are not just mathematical models, where one starts from axioms and ends up with predictions of the theory. The models are chosen to describe known data, their predictions are checked continuously agains new data . Isospin, particle exchanges etc are all in the lagrangian and quantum field theory tools are used to calculate crossections etc to be checked by future data. Th SM developed over the years after observing the symmetries that existed in the experimental data , for example the eightfold way which led to the proposal of the quarks . The symmetries disclosed by the data led to the SM Lagrangian which was chosen to display these symmetries of SU(3)xSU(2)xU(1) .

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+1 for the SM summary PDF –  Love Learning Apr 19 at 21:21

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