Peskin and Schroeder eq. 18.84

In summary, the student is self-studying the book of Peskin&Schroeder and has a question about a numerical factor in equations 18.80 and 18.84. They are wondering about the extra factor of 2 in equation 18.84 and believe they understand the rest of the calculation. The equations are related by the optical theorem and one is for ##e^+e^-\rightarrow e^+e^-## while the other is for ##e^+e^-\rightarrow \text{hadrons}##.
  • #1
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Homework Statement


So I am self-studying the book of Peskin&Schroeder, and there is something I don't understand on page 616.

In eq. 18.80, there is a numerical factor of ½ and going from e2 to α will introduce a factor 4π when proceeding to eq. 18.84. But then there should be a numerical factor of 2π in eq 18.84. What gives an extra factor of 2?

Homework Equations


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(this is the first time I post here, please do tell if uploading a page in this format is not acceptable)

The Attempt at a Solution



I believe I understand the rest of the calculation on this page.
 
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  • #2
Well, equation (18.80) is for ##e^+e^-\rightarrow e^+e^-##, equation (18.84) is for ##e^+e^-\rightarrow \text{hadrons}##. As the text says, the two are related by the optical theorem.
 

Related to Peskin and Schroeder eq. 18.84

1. What is the significance of Peskin and Schroeder equation 18.84?

Equation 18.84 in Peskin and Schroeder's book "An Introduction to Quantum Field Theory" is a crucial equation for calculating scattering amplitudes in quantum field theory. It represents the transition amplitude for a particle to travel from one point to another in space-time.

2. Can you explain the terms used in equation 18.84?

The terms used in equation 18.84 represent the initial and final states of the particle, as well as the interaction Hamiltonian. The equation also includes the propagator, which describes the probability amplitude for the particle to travel from one point to another in space-time.

3. How is equation 18.84 derived?

Equation 18.84 is derived using the principles of quantum mechanics and quantum field theory. It is based on the Feynman path integral, which allows for the calculation of transition amplitudes by summing over all possible paths that a particle can take from one point to another in space-time.

4. What is the physical meaning of equation 18.84?

The physical meaning of equation 18.84 is that it represents the probability amplitude for a particle to travel from one point to another in space-time, taking into account all possible paths that the particle can take. This allows for the calculation of scattering amplitudes and other important quantities in quantum field theory.

5. How is equation 18.84 used in practical applications?

Equation 18.84 is used in practical applications to calculate scattering amplitudes and other important quantities in quantum field theory. It is also used in theoretical research for making predictions and testing the validity of different theories in particle physics.

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