Why do multiparticle states present continuous in spectral function?

In summary, the Peskin QFT book states that one-particle states appear as a delta function in the spectral function at s=m^2, while multiparticle states appear as a continuous form starting at s=4m^2. However, the reason for this difference is not fully understood. Can someone provide a clearer explanation from a mathematical or physical perspective? In terms of physics, if we have two particles with equal and opposite three-momentum, their total energy can range from E=2m to infinity, while their total three-momentum is always zero. This applies similarly to systems with 3 or more particles.
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I have learned the fact from Peskin QFT book,that one-particle state presents a delta function form in spectral function at s=m^2,while multiparticle states present a continuous form begin at s=4m^2,but i don't really understand the reason.What cause the difference between one-particle state and multiparticle states?Could someone explain this a bit clearer from the viewpoint of mathematics or physics or both?
 
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Physically, if we have two particles, we can give them equal and opposite three-momentum (of any magnitude). Then their total three-momentum is zero, but their total energy varies continuously from E=2m (when they each have zero three-momentum) up to infinity. Similarly with 3 or more particles.
 

1. Why do multiparticle states present continuous in spectral function?

Multiparticle states present continuous in spectral function because they are composed of multiple particles with different energies. This results in a range of possible energy values, rather than a single discrete energy level.

2. How is the spectral function related to the multiparticle states?

The spectral function is a mathematical function that describes the distribution of energy levels in a system. It is related to multiparticle states because it shows the range of possible energy values for these states.

3. Can multiparticle states have a discrete spectral function?

No, multiparticle states cannot have a discrete spectral function because they are composed of multiple particles with different energy levels. This results in a continuous range of energy values rather than a discrete set of energy levels.

4. What is the significance of continuous spectral function in multiparticle states?

The continuous spectral function in multiparticle states is significant because it reflects the underlying complexity and interactions of the particles within the system. It also allows for a more accurate representation of the energy distribution in these states.

5. How is the continuous spectral function experimentally observed in multiparticle states?

The continuous spectral function in multiparticle states can be observed experimentally through techniques such as spectroscopy, which measures the energy levels of particles in a system. These measurements can then be used to construct a spectral function and observe its continuous nature.

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