In QFT, when the scattering process occur, the mass does not conserved in off-shell.
What I'm curious about is whether the angular momentum is conserved or not in off-shell.
Thank you for answering this question.
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"the mass does not conserved in off-shell."
This is a misunderstanding, there is no conservation of mass. Elementary particles have fixed mass , given in the table, and stable quantum mechanical solutions of a system of particles, as protons and neutrons have the mass given by the four vector that describes the system also fixed.
There is conservation of momentum , energy, angular momentum and quamtum numbers. If you are talking of virtual particles, yes, they are off mass shell under the integration BUT they have all the other quantum numbers that their names carry, including spin, that is why they keep their name. It will depend on the specific Feynman diagram how the conservation of angular momentum happens in an interaction.