Towards Infrared Finite S-matrix in Quantum Field Theory by Hayato Hirai

Author:Hayato Hirai
Language: eng
Format: epub
ISBN: 9789811630453
Publisher: Springer Singapore

(3.1)

where stands for all the internal parameters characterizing the state: total momentum, relative momentum of different d.o.f, spins, charges, etc. However, the quantum states with definite momentum are not spatially localized waves, rather spread out all over the space due to the uncertainty principle. Therefore, they are not the particles observed in the scattering experiments because they do not satisfy the assumption I. Moreover, they do not change at all during the time evolution because the time evolution is generated by and it just gives the irrelevant over all phase to . Therefore, they are not the states describing the scattering processes that generally involve complicated time evolutions. To satisfy the assumption, the wave must be the wave packet that is the superposition of many waves with different momentum(i.e., wave length). We write the state of wave packets as

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