Imagine that you are a 973 chief scientist, and your project is to simulate a glass of water with a brilliant supercomputer to see how much resistance there is to slowly pull the iron ball inside. Your idea is simple: directly and accurately simulate each water molecule! You input the real size (one parameter), shape (for example, described by 2 parameters) and force at different distances (and used 2 parameters) of water molecules into the computer, and your supercomputer is awesome, directly simulating 1 26 water molecules. Then you put the iron ball into the mold, and calculated the resistance that needs to be overcome to make the iron ball move slowly by means of calculation and simulation. Compared with the experiment, we found an exact match! I'm so happy, as long as I simulate it a few more times and save more data, I can send nature. At this time, the system administrator sends you an email, saying that you take up too much cpu time and others can't do anything. Let you find a way to reduce the amount of calculation. What should we do? You think about it and think that the iron ball is so big that you can get the correct answer without making the simulation so detailed. So you decided to increase the volume of water molecules for simulation by 1 times, so you only need to simulate 1 25 molecules. However, if we can't do this alone, the results will definitely be wrong, because some small movements at the nanometer level have lost their macro effects. At this time, one of your students said, Boss, in fact, we can try to change the other 4 parameters, and maybe we can make up for what we lost. You think it's reliable, start your smart brain and think about it, and mentally calculate the changes needed for each parameter. So you recalculate with larger molecules and new parameters, and accurately reproduce the data obtained before. (Note that at this time, you have already renormalized your system.)

The system administrator thinks you are easy to bully and asks you to reduce the resources you occupy. With a wave of your hand, you said, "It's simple, I can reduce the cpu time to 1/1", and you repeated the process of increasing the molecular size and adjusting the parameters for 1 times. Now your molecular volume is 1-11 times larger than that of real water molecules, but you still calculated the resistance that is in good agreement with the experiment. In your nature article, this method invented to simplify calculation is called Renormalization group (RG). Call the size of water molecules in each simulation RG scale, and then you list the parameters used each time according to the size of water molecules, and call their changes as the size increases RG running of parameters. You foresee the application of field theory, and call this new model obtained by this method Low Energy Effective Field Theory (EFT). Finally, you are a little surprised to find that when you increase the size of water molecules step by step, some of the 4 parameters that were originally critical simply become , and some parameters are directly proportional to other parameters. In short, in the end, you only used about 1 free parameters to describe this glass of water perfectly. You call those last useless parameters IRREFERENT PARAMETERS and the shape/force they describe irrelevant operator. You remove all these irrelevant parameter/operator, and the simplified theoretical model you get is called renormalizable theory. It is almost the same as the EFT you got before.

At this time, the system administrator came to bully you again and said, can you just simulate two water molecules so that he can play games with supercomputing? But this time, you spread your hands and said, dude, this is really not good. If my water molecule is bigger than my iron ball, then no matter how to adjust the parameters, my calculation will definitely fail, and the next science will not be published! (In the case of water molecules, RG scale should not be close to the size of iron balls. In real field theory, there are technologies that allow RG scale to be selected to be equivalent to the size of physical processes. But in any case, RG scale should not be longer than the size of physical process. )