Peskin and Schroeder - page 4 - choice of notation

In summary, Peskin and Schroeder's diagram in page 4 depicts the collision of an electron and positron beam resulting in the production of ##\mu^{+}## and ##\mu^{-}## beams. The diagram shows that the electron and positron beams have momenta ##\textbf{p}## and ##\textbf{p}'##, while the muon beams have momenta ##\textbf{k}## and ##\textbf{k}'##. This use of different symbols for momenta is a matter of notational difference and as long as it is clearly defined, it can be used interchangeably. In natural units where ##\hbar=1##, different symbols are often used to
  • #1
spaghetti3451
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In page 4, Peskin and Schroeder has the following diagram:

Capture.jpg


The diagram shows the collision of an electron beam and a positron beam to produce a ##\mu^{+}## beam a ##\mu^{-}## beam.

My question is this:

The electron and positron beams are shown to have momenta ##\textbf{p}## and ##\textbf{p}'##.

But the muon beams are shown to have momenta ##\textbf{k}## and ##\textbf{k}'##.

##\textbf{p}## is standard notation for momentum, but ##\textbf{k}## is standard notation for wavevector. But then, in natural units, ##\hbar=1##.

Therefore, is the different use of symbols for momenta a matter of notational difference, or is there some underlying physics I am missing?
 
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  • #2
You can call things whatever you like as long as you define what is meant. Throughout PS you will notice p, k, and q being used to denote different momenta (and more importantly, 4-momenta) simply for the reason that the others are being used to denote something else in the particular context.
 
  • #3
Thanks! :)
 

FAQ: Peskin and Schroeder - page 4 - choice of notation

1. What is the purpose of using different notations in Peskin and Schroeder?

The choice of notation in Peskin and Schroeder is intended to provide a clearer and more concise way of representing complex mathematical equations in quantum field theory. It allows for a more systematic and organized approach to solving problems and understanding concepts.

2. How many different notations are used in Peskin and Schroeder?

Peskin and Schroeder primarily use three different notations: the Dirac notation, the Feynman slash notation, and the Einstein summation convention. These notations are commonly used in quantum field theory and are essential in understanding the mathematical formulas presented in the book.

3. Can I use my own notation while studying Peskin and Schroeder?

Yes, you can use your own notation while studying Peskin and Schroeder. However, it is recommended to stick to the notations used in the book to avoid confusion and ensure consistency in your understanding of the material.

4. Do I need to have a strong mathematical background to understand the notations in Peskin and Schroeder?

While a strong mathematical background is helpful in understanding the notations used in Peskin and Schroeder, it is not a requirement. The book provides a thorough explanation of the notations and their applications, making it accessible to readers with varying levels of mathematical knowledge.

5. Are the notations in Peskin and Schroeder used in other areas of physics?

Yes, the notations used in Peskin and Schroeder are commonly used in other areas of physics, particularly in quantum mechanics and quantum field theory. Familiarizing yourself with these notations will not only help in understanding the book but also in future studies and research in these fields.

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