Longitudinal polarization in Feynman photon propagator?

In summary, longitudinal polarization in the Feynman photon propagator refers to the orientation of the electric and magnetic fields of a photon as it travels through space. It is different from transverse polarization, which describes perpendicular orientation, and plays a crucial role in calculating scattering amplitudes in Feynman diagrams. The inclusion of longitudinal polarization can affect the renormalizability of quantum field theories and can be experimentally observed in high-energy particle collisions. However, it is often challenging to directly measure and other techniques are used to study it.
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copernicus1
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For internal photon states, is it necessary to sum over the longitudinal polarization state in addition to the transverse states? And if so, does the ordinary Feynman-gauge propagator take care of this?

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No. However, the longitudinal states do not couple to the conserved electromagnetic current, so it doesn't matter whether you include them or not. Thus the ##k^\mu k^\nu## term in the propagator can be multiplied by an arbitrary number (this is sometimes called "generalized Feynman gauge"), and the scattering amplitudes do not depend on that number.
 
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Related to Longitudinal polarization in Feynman photon propagator?

1. What is longitudinal polarization in the Feynman photon propagator?

Longitudinal polarization refers to the orientation of the electric and magnetic fields of a photon as it propagates through space. In the Feynman photon propagator, it describes the probability of a photon with a specific momentum and energy to travel from one point to another.

2. How is longitudinal polarization different from transverse polarization?

Transverse polarization describes the perpendicular orientation of the electric and magnetic fields of a photon, while longitudinal polarization describes the parallel orientation. In the Feynman photon propagator, transverse polarization dominates, but longitudinal polarization becomes important at high energies.

3. What is the significance of longitudinal polarization in Feynman diagrams?

Longitudinal polarization plays a crucial role in the calculation of scattering amplitudes in Feynman diagrams. It can affect the overall strength and behavior of interactions between particles, particularly at high energies. Understanding and accurately representing longitudinal polarization is important for making precise predictions in particle physics.

4. How does the inclusion of longitudinal polarization affect the renormalizability of quantum field theories?

The inclusion of longitudinal polarization in Feynman diagrams can lead to ultraviolet divergences, which can make quantum field theories non-renormalizable. This is because longitudinal polarization can contribute to the overall strength of interactions, making the theory less predictive. Thus, renormalization techniques must be applied to account for these divergences.

5. Can longitudinal polarization be experimentally observed?

Yes, longitudinal polarization can be observed in various experiments, particularly in high-energy particle collisions. For example, the Large Hadron Collider (LHC) at CERN has observed evidence of longitudinal polarization in certain scattering processes. However, it can be challenging to directly measure longitudinal polarization, and other techniques such as indirect measurements and theoretical calculations are often used.

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