# Notation of $\delta$ meaning [duplicate]

In the Leonard Susskind Lectures on Classical Mechanics on youtube, while he disusses symmetry and its relation to conservation laws, he uses the notation $$\delta$$ to refer to a certain "small quantity", but then again he uses it in a sense of operator (variation, eg. $$\delta S$$ is the variation in the action) which is proportional to the quantity $$\delta$$. Please help in clarifying this, I may have understood something pretty badly.

• I asked a question about this and similar notation forms a while back and got this great answer from Kyle Kanos: physics.stackexchange.com/a/153798/4962. Seems that there are multiple meanings of several of such symbols. Jan 13 at 12:23
• Yup I saw that, but it wasn't dealing with the "small quantity" concept. But thanks for the reference Jan 13 at 15:29

In this context, $$\delta$$ can have two meanings depending on where it's used. When $$\delta$$ is alone, it represents a small quantity, as you described - for example, shifting $$f(x)$$ to the right by a small amount could be represented by $$f(x-\delta)$$.
When $$\delta$$ is accompanied by another letter, for example $$\delta S$$, that represents a small shift in that variable. This is, as you say, the variation in the action $$S$$. If you want to consider what happens to a system that depends on position $$\vec{x}$$ when you shift that position by a small amount, you might consider a new coordinate system defined by $$\vec{x}\rightarrow\vec{x}+\delta\vec{x}$$.
The symbol $$\delta$$ can have multiple different meanings. One thing to be aware of would be if you want to multiply a small quantity $$\delta$$ by a variable $$x$$; I'd usually express that as $$x\delta$$ or $$\delta\times x$$.