Understanding Particle Poles in Amplitude Expressions: Explained

[Sombrero]

Gents I have one question:

If I have expresion for amplitude of some process and this amplitude has pole, I say I have particle caryring such features (suppose mass that makes this pole), if I change some parameters in expression for amplitude and if I get another pole, I say in this case there is particle having anothe features. So my question is why poles in expressions correspond to particles?

Thanks

 

[Perturbation]

Because the field theory describes the dynamics of particles with a mass m. The pole comes from the equality of the norm of the four-momentum and square of the mass in the denominator. The quantised field will only create particles with mass m but the norm norm of the four-momentum of the field at some point doesn't have to be equal to the square of the physical mass of the particle it describes.

 

[denian]

for your question. The concept of particle poles in amplitude expressions is closely related to the idea of resonance in particle physics. When a particle decays or interacts with other particles, it can do so through a resonance process, where the energy of the system matches the mass of a particle. This results in a peak in the amplitude expression, or a pole, which represents the resonance.

In other words, the presence of a pole in the amplitude expression indicates the existence of a particle with a specific mass and other properties that allow it to interact with other particles in a specific way. By changing the parameters in the amplitude expression, we can observe different poles, indicating the existence of different particles with different properties.

Furthermore, the poles in amplitude expressions are related to the complex poles in the scattering matrix, which is a fundamental concept in quantum field theory. The location of these poles in the complex plane corresponds to the mass and lifetime of the particle.

In summary, the poles in amplitude expressions correspond to particles because they represent the resonant behavior of particles in interactions and are related to the complex poles in the scattering matrix. This understanding of particle poles is crucial in understanding the behavior of particles and their interactions in the field of particle physics.