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.

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    $\begingroup$ 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. $\endgroup$
    – Steeven
    Jan 13 at 12:23
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    $\begingroup$ Yup I saw that, but it wasn't dealing with the "small quantity" concept. But thanks for the reference $\endgroup$ 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 $\delta\times x$.

  • $\begingroup$ Alright, that clarifies! $\endgroup$ Jan 13 at 15:27

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