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

• I
• swampwiz
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.
swampwiz
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.

And I always thought that ##\delta## was Dirac's delta

The same symbol can have different meaning in different contexts.

fresh_42 and topsquark
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.

## 1. What is the small Greek delta letter used for in science?

The small Greek delta letter (δ) is often used to represent the concept of a differential in mathematics and science. It can also represent change or variation in a quantity.

## 2. How is the small Greek delta letter different from the English letter "d"?

The small Greek delta letter is often used to represent a partial derivative, while the English letter "d" is used for a total derivative. This means that the small Greek delta letter represents a change in one variable while holding all other variables constant, while "d" represents a change in all variables.

## 3. Can the small Greek delta letter be used in other fields besides math and science?

Yes, the small Greek delta letter is also used in other fields such as economics, engineering, and physics. In economics, it can represent a change in demand or supply, while in engineering it can represent a change in voltage or current. In physics, it can represent a change in position or momentum.

## 4. Is the small Greek delta letter always used to represent a change or difference?

No, the small Greek delta letter can also be used to represent other concepts, such as the discriminant in quadratic equations or the relative difference between two values. Its meaning may vary depending on the context in which it is used.

## 5. Are there any other symbols that can represent a differential?

Yes, there are other symbols that can represent a differential, such as the lowercase letter "d" with a line through it (đ), which is used in thermodynamics, or the symbol "∂" (partial derivative symbol), which is used in vector calculus. However, the small Greek delta letter is the most commonly used symbol for representing a differential in mathematics and science.

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