In particle physics their are several quantities (charge, baryon number, lepton number, momentum, and energy) which are conserved by all 4 fundamental interactions. Often in textbooks etc. their are questions asking whether a particular interaction can occur. e.g. $$A +B \rightarrow X+Y$$ I usually do such questions by seeing if any of the above conservations laws have been violated, and if they haven't stating that it can occur. But this got me thinking, is it in fact a necessary and sufficient condition for an interaction to have a non-zero probability of occurring that these conservations laws are satisfied? Or are their interactions that have a zero probability but do satisfy these conservations law? Please can you explain your answer.
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