Conserved quantities in the Feynman diagrams.

[naggy]

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?

 

[tiny-tim]

hi naggy!

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)

 

[tom.stoer]

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.

 

[naggy]

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 ...

 

[tom.stoer]

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.