I have beening trying my best to understand the notion of fields in Quantum field theory. Here are some questions that I have out of 100... 1)What is the conceptual way of understanding the locality of fields? 2)How to calculate fields?(in dim 2 case) 3)Will the calculation depends on the worldsheet metric or signature? For 2), why the following calculation is wrong? In dim 1 case(only time parameter), since field must satisfy the field equation, so it should look like: exp(itH)Oexp(-itH) where H is the hamiltonian from time translation invariance. Thus in dim 2 case, the field should be: exp(isP)exp(itH)Oexp(-itH)exp(-isP) where P comes from the translation invariance in the circle direction.