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I want to know what mathematical theories I should be aware of for a deep understanding of the standard particles model.

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marked as duplicate by Emilio Pisanty, JamalS, jinawee, Neuneck, Qmechanic May 26 '14 at 12:30

This question was marked as an exact duplicate of an existing question.

This sort of question is too broad for our format. Additionally, this particular one has been asked a million times before. – Emilio Pisanty May 26 '14 at 11:33
As Emilio rightly stated, the question is too broad. If you're asking to learn the Standard Model, just master the content of Peskin and Schroeder, you can garner the mathematical prerequisites by skimming the text. Afterwards, watch Perimeter's lectures on the Standard Model by Professor Mark Wise; they're excellent and quirky as well. – JamalS May 26 '14 at 11:49

This depends on what you already know, but if you know some quantum field theory, then getting to know the $SU(N)$ groups is a good start.

This is because the standard model is built upon Gauge-symmetry under these groups. The symmetry group of the standard model is:

$$SU(3) \times SU(2) \times U(1)$$

The $SU(3)$ is the symmetry of the strong force under the echange of colour. The $SU(2) \times U(1)$ is the symmetry group of the electroweak sector.

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