It will be shown that the notions of space and time in axiomatic quantum field theory arise from translation symmetry. The possibility of using this construction in string theory will be discussed.
The derivation of the notion of space and time can be applied also to the case when the tranlation symmetry is discrete. It seems that in the case of discrete symmetry group it is natural to assume that all basic physical quantities are integer or, at least, rational, and real numbers should be used only for mathematical convenience. If this is the case then one can conjecture that sometimes should be useful to work with p-adic numbers instead of real numbers. I'll explain how this idea worked in my recent papers written in collaboration with Kontsevich, Vologodsky and Shapiro.