Although one should not require 科普 to be very accurate, your work has too
many fundamental errors. I support your good wish to proivde some basic
knowledge of high energy to those who are not working in that field, but it
seems that you are not familar with high energy theory at all. I think it is
not responsible to say something that you don't understand, without tell
the readers that this is only your understanding of the problem. And very
unfortunately, your understanding is not the picture accepted by most
theoriest.
In this particular work, your explanations about local symmetry, global
symmetry and symmetries broken by quantum anormaly are all wrong. Although
most physical terms are right, your understandings about most of them are
wrong.
You said local symmtries are ture symmetry but global symmtries are usualy
not. This is not right. Whether a symmetry is a true symmetry or an
approximate symmetry has nothing to do with whether it is a local or global
symmetry. There are approximate gauge symmetries (not in the standard model
but there are examples in condensed matter and other places) and there are
many examples of true global symmetries.
You said that those approximate symmetry may be broken by quantum flucations
. This statement is wrong. Your are confusing two totally unrelated things.
An approximate symmetry is just an approximation. No matter in quantum
thoery or in a classical one, one will find that the symmetry is not exact.
On the other hand, for true symmetries, quantum fluctuations may break some
true symmetry by anormalies. However, it is just opposite to what you said.
Usually, these kind of examples are local symmetries, instead of gobal.
Although the effect seem similar, they are totally different mechanics. You
will understand the difference after reading any serious field theory book.