Peskin and Schroeder - page 4 - choice of notation

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The discussion revolves around the notation used in Peskin and Schroeder's diagram on page 4, which depicts the collision of electron and positron beams producing muon beams. The question raised concerns the use of different symbols for momenta, specifically ##\textbf{p}## for electrons and positrons, and ##\textbf{k}## for muons, noting that ##\textbf{k}## typically denotes wavevector. It is clarified that in natural units, where ##\hbar=1##, the distinction in notation is not a matter of underlying physics but rather a contextual choice to avoid confusion. The use of various symbols like p, k, and q throughout the text serves to delineate different momenta and 4-momenta based on the context. This approach allows for clearer communication of concepts without losing precision in the definitions.
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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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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.
 
Thanks! :)
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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