Feynman Propagators: Invariant Amplitude vs Loop Integrals

Thread starter ryanwilk
Start date Jan 11, 2012
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Feynman Propagators

In summary, the Feynman propagator is a mathematical tool used in quantum field theory to calculate the probability amplitude of particle interactions. It takes into account the effects of virtual particles and their anti-particles, using perturbation theory to incorporate these effects. While it can be applied to all particles in theory, it may not accurately describe all interactions and can be complex and time-consuming for multiple particles and higher order terms. Alternative methods have been developed to calculate particle interactions.

Jan 11, 2012

ryanwilk

Hi, this is probably very simple but what is the difference between these two Feynman propagators:

[tex] \frac{i}{q^2-m^2}[/tex]
[tex] \frac{i(p/+m)}{p^2-m^2}[/tex]

E.g. Is one used for the invariant amplitude and the other for loop integrals? Or is one for a fermion and the other for a boson? =s

Thanks!

Last edited: Jan 11, 2012

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Jan 11, 2012

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The top one is for a scalar, the bottom one for a spin-1/2 particle.

Jan 11, 2012

ryanwilk

Thank you!

1. What is the purpose of the Feynman propagator?

The Feynman propagator is a mathematical tool used in quantum field theory to calculate the probability amplitude of a particle propagating from one point in space-time to another. It takes into account the effects of both virtual particles and their anti-particles, allowing for a more accurate calculation of particle interactions.

2. What is the difference between the invariant amplitude and loop integrals in the Feynman propagator?

The invariant amplitude in the Feynman propagator is a representation of the probability amplitude for a particle to travel from one point to another in space-time. It is calculated using the Feynman path integral, which sums over all possible paths the particle could take. On the other hand, the loop integrals in the Feynman propagator take into account virtual particle interactions and are used to calculate the overall probability amplitude for a particle interaction.

3. How does the Feynman propagator account for the effects of virtual particles?

The Feynman propagator uses a mathematical technique known as perturbation theory to incorporate the effects of virtual particles. This involves calculating the probability amplitude of a particle interaction as a series of terms, with each term representing a different order of virtual particle interaction. By including higher order terms, the Feynman propagator can account for the effects of virtual particles on the overall probability amplitude.

4. Can the Feynman propagator be applied to all particles in quantum field theory?

Yes, the Feynman propagator can be applied to all particles in quantum field theory, including both elementary particles and composite particles. It is a fundamental tool used in many calculations in particle physics and has been successfully applied to a wide range of particle interactions.

5. What are the limitations of using the Feynman propagator?

One limitation of the Feynman propagator is that it is based on perturbation theory, which may not accurately describe all particle interactions. In addition, the calculations involved in the Feynman propagator can become extremely complex and time-consuming for interactions involving multiple particles and higher order terms. As a result, alternative methods have been developed to calculate particle interactions, such as lattice field theory and Monte Carlo simulations.