What kind of differential does the small Greek delta letter represent?

In summary, the symbol δ can have different meanings depending on the context in which it is used. In the context of differential elements, it represents a parameter that is not meant to be a well-defined function, while in the context of calculus of variations, it represents a function whose input variable is a path. It can also represent "something small" in other contexts, such as in the study of Lie groups and one-parameter groups.
  • #1
swampwiz
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δ

I had always thought that it represents a differential element for a parameter that it is not supposed to be a well-defined function - e.g., for a differential or heat or work in thermodynamics - as opposed to a regular Latin d, which is supposed to be such a well-defined function. However, Sabina Hossenfelder says here that it means a differential that is meant to be a function whose input variable is a path, which sounds like something out of calculus of variations.

 
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  • #2
And I always thought that ##\delta## was Dirac's delta :smile:

The same symbol can have different meaning in different contexts.
 
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  • #3
swampwiz said:
δ

I had always thought that it represents a differential element for a parameter that it is not supposed to be a well-defined function - e.g., for a differential or heat or work in thermodynamics - as opposed to a regular Latin d, which is supposed to be such a well-defined function. However, Sabina Hossenfelder says here that it means a differential that is meant to be a function whose input variable is a path, which sounds like something out of calculus of variations.

Here is an example that fits into the context:
https://www.physicsforums.com/insights/when-lie-groups-became-physics/
It is basically how it was used in:
A. Cohen, An Introduction to Lie Theory of One-Parameter Groups, Baltimore 1911

At least, it shows that "something small" is the answer in the given context.
 

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