Graduate What Drives the Naming and Structure of One-Particle Irreducible Diagrams?

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SUMMARY

One-particle irreducible diagrams are defined as diagrams that cannot be separated into two disconnected diagrams by cutting an internal propagator. The truncation of external lines in these diagrams is essential for their application in scattering calculations. The term 'one-particle' is used to distinguish these diagrams from k-particle irreducible diagrams, which involve correlations among k particles and are crucial for nonequilibrium quantum field theory calculations.

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spaghetti3451
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One-particle irreducible diagrams are diagrams that cannot be broken into two disconnected diagrams by cutting an internal propagator.1. Why are the external lines on an one-particle irreducible diagram truncated/amputated?

2. What is the motivation for the word 'one-particle' in the terminology?
 
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spaghetti3451 said:
1. Why are the external lines on an one-particle irreducible diagram truncated/amputated?
because that's how they are used in scattering calculations.
spaghetti3451 said:
2. What is the motivation for the word 'one-particle' in the terminology?
One also defines ##k##-particle irreducible diagrams (which cannot be made disconnected by removing up to ##k## internal lines). These describe the properties of ##k##-point correlations (involving ##k## particles, hence the name), which are important for calculations in nonequilibrium quantum field theory.
 
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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