Possibly the most useful thing anyone could tell me about particle physics:
Naively, one could try and make an algebra by enumerating all the types of particles and defining equivalence relationships (some rules), for example
object type 1: photon
object type 2: electron
object type 3 ...
object type n
rule 1: a photon is equivalent to an electron and a positron
rule 2: a proton is equivalent to three quarks
Then one could study the properties of these relationships as a mathematical structure containing objects that represent particles and rules that define equivalence - i.e. as an algebra. I assume such an algebra would be, if formulated correctly, represented by Feynman diagrams (for some particles at least). Does such an algebra have a name? Is there more than one? Is this at all connected to the idea behind stating that the standard model is U(1) x SU(2) x SU(3)?
By an algebra I understand a closed and consistent collection of mathematical objects and relationships.
Thanks for trying to understand what I'm asking, with your input I can aim to make this more comprehensible. So I guess I'm looking for a formal structure which reflects particle reactions which is abstracted away from spatial, temporal and energetic considerations as far as is possible (is it at all possible?).