Notation Convention: Primes in Coordinate Transformations

In summary, the convention for denoting a tensor represented in a new frame is to put primes on the indices, such as x^{\mu'}. This helps clarify which indices have been transformed to the new frame.
  • #1
Steely Dan
319
0
I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is

[tex]x^{\mu}[/tex]

then this four-vector in a different frame is often written as either

[tex] x'^{\mu} [/tex]
or
[tex] x^{\mu}{'} [/tex]

Is there a recommended convention for this, or better yet, is one of them substantially more common than the other?
 
Last edited:
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  • #2
I think the more common convention is to put primes on indices, like so:

[tex]x^{\mu'}[/tex]

This way, it is clear exactly which indices have been transformed to a new frame.
 

Related to Notation Convention: Primes in Coordinate Transformations

1. What is the purpose of using primes in coordinate transformations?

The use of primes in coordinate transformations is a notation convention used to distinguish between the original coordinates and the transformed coordinates. It helps to avoid confusion and clearly indicate which coordinates are being referred to in a particular equation or problem.

2. How are primes typically used in coordinate transformations?

In most cases, primes are used to represent the transformed coordinates. For example, if the original coordinates are denoted as (x, y), the transformed coordinates may be denoted as (x', y'). This indicates that the coordinates have been transformed in some way.

3. Are there any other conventions for representing transformed coordinates?

Yes, there are other conventions such as using a tilde (~) or a hat (^) to represent transformed coordinates. However, the use of primes is the most common and widely accepted convention.

4. Can primes be used for other purposes in mathematics?

Yes, primes have various uses in mathematics. In addition to representing transformed coordinates, they are also commonly used to denote prime numbers, indicate derivatives in calculus, and mark the number of iterations in mathematical sequences.

5. Is it necessary to always use primes in coordinate transformations?

No, the use of primes is not mandatory in coordinate transformations. Some equations or problems may not require them, and other notation conventions may be used instead. It ultimately depends on the preferences of the mathematician or scientist conducting the analysis.

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