Peskin/schroeder RG flow diagram

In summary, the Peskin/Schroeder RG flow diagram is a graphical representation of the renormalization group flow in quantum field theory. It is constructed by plotting the renormalization group equation on a two-dimensional plane and provides information about the behavior of a theory at different energy scales. The RG flow diagram can also be used to make predictions and compare them to experimental data. However, it has limitations such as assuming the system is in thermal equilibrium and not providing precise values of coupling constants.
  • #1
geoduck
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On page 403, diagram 12.1 (b) of Peskin and Schroeder, does anyone know why the coupling constant at first increases to the right, and then all of a sudden decreases to left until it reaches the fixed point zero?

According to equation 12.28, as b→0, the coupling decreases monotonically. So shouldn't the coupling always be decreasing?
 
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  • #2
I think it's just the perspective. The curves are supposed to be in the m^2 = 0 plane.
 
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FAQ: Peskin/schroeder RG flow diagram

What is the purpose of the Peskin/Schroeder RG flow diagram?

The Peskin/Schroeder RG flow diagram is a graphical representation of the renormalization group (RG) flow in quantum field theory. It is used to study the behavior of physical systems at different length scales and to understand how the parameters of a theory change under the process of renormalization.

How is the RG flow diagram constructed?

The RG flow diagram is constructed by plotting the renormalization group equation on a two-dimensional plane, with one axis representing the energy scale and the other representing the coupling strength. A trajectory is then traced by varying the energy scale and observing how the coupling strength changes.

What information can be obtained from the RG flow diagram?

The RG flow diagram provides information about the behavior of a theory at different energy scales. It can show if a theory is asymptotically free or conformal, and can also reveal the existence of fixed points where the coupling strength remains constant. Additionally, it can demonstrate the stability or instability of a theory under renormalization.

How does the RG flow diagram relate to experimental results?

The RG flow diagram can be used to make predictions about the behavior of a physical system at different energy scales, which can then be compared to experimental data. By studying the RG flow, physicists can make connections between the microscopic and macroscopic properties of a system.

Are there any limitations to the RG flow diagram?

While the RG flow diagram is a useful tool for understanding the behavior of physical systems, it does have some limitations. It assumes that the system is in thermal equilibrium and that all interactions are weak, which may not always be the case. Additionally, the diagram does not provide information about the precise values of the coupling constants, only their behavior under renormalization.

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