Conserved quantities in the Feynman diagrams.

In summary, Feynman diagrams represent the conservation of 3-momentum and spin in position representation and 4-momentum and spin in momentum representation at each node. Over the entire diagram, unitarity and usually all other currents and charges are conserved. However, for certain global symmetries, there may be violations of these conservations due to divergent terms.
  • #1
naggy
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I'm currently reading Griffiths book (I'm at chapter 4) on Particle physics, and I had a question about Feynman diagrams.

In every "node" of a Feynman diagram, what quantities are conserved?

Further, what quantities are conserved over the entire diagram?
 
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  • #2
hi naggy! :wink:
naggy said:
In every "node" of a Feynman diagram, what quantities are conserved?

in position representation, 3-momentum (and spin etc)

in momentum representation, 4-momentum (and spin etc)
Further, what quantities are conserved over the entire diagram?

as a whole, the diagram represents reality, so 4-momentum (and spin etc) :smile:
 
  • #3
Of course 4-momentum and spin.

Unitarity is conserved over the sum of all Feynman diagrams.

Usually all other currents (and charges) are conserved; it can happen that a current becomes anomalous which means that during quantization it's quantized version of the continuity equation (Ward identities) is violated. For gauge symmetries this is forbidden, but for certazin global symmetries it may be allowed. In order to save el.-mag. U(1) symmetry one has to allow for a violation of the axial current Ward identity in the famous triangle anomaly.
 
  • #4
Seems to me from the book that every property of the particle is conserved on the node. Or am I drawing the wrong conclusion?

momentum, charge, Spin, Isospin, Hypercharge, strangeness, baryon number, lepton number, color ...
 
Last edited:
  • #5
You cannot draw this conclusion for the whole diagram as it may contain divergent terms which - after renormalization - violate certain global symmetries. This is shown explicitly for the triangle anomaly.
 

1. What are conserved quantities in Feynman diagrams?

Conserved quantities in Feynman diagrams refer to physical quantities that remain constant throughout a particle interaction. These quantities include energy, momentum, and charge.

2. How are conserved quantities shown in Feynman diagrams?

In Feynman diagrams, conserved quantities are represented by arrows pointing in the direction of the particle's momentum and labeled with the particle's charge. These arrows are connected by lines representing the particles' interactions.

3. Why are conserved quantities important in Feynman diagrams?

Conserved quantities play a crucial role in Feynman diagrams as they help to explain and predict the outcome of particle interactions. They also provide a way to check the accuracy of calculations and ensure that the laws of conservation are being upheld.

4. Can conserved quantities ever be violated in Feynman diagrams?

In theory, conserved quantities should always be conserved in Feynman diagrams. However, there are instances where they may appear to be violated due to uncertainties in measurements and calculations. These cases are usually resolved by taking into account other factors or including higher-order effects.

5. How do conserved quantities in Feynman diagrams relate to fundamental laws of physics?

Conserved quantities in Feynman diagrams reflect the fundamental laws of physics, such as the law of conservation of energy and the law of conservation of momentum. These laws are crucial in understanding the behavior of particles and their interactions, and their conservation is a fundamental principle in physics.

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