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prajor

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- Thread starter prajor
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In summary, the conversation discusses the representation of positrons in feynman diagrams and their interpretation in quantum field theory. Originally, it was thought that positrons traveled backwards in time and represented negative energy solutions, but this was quickly realized to be incorrect. Dirac proposed the "hole theory" where positrons were seen as unoccupied negative energy levels, but this theory was also found to be flawed. The current understanding is that positrons are represented by positive energy states and the idea of them traveling backwards in time is incorrect. There are no negative energy states in the Hilbert space. There is a comprehensive source, a paper titled "Relativistic Quantum Mechanics of Fields" that discusses this topic in depth.

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prajor

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- #2

Bill_K

Science Advisor

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Originally it was thought that relativistic quantum mechanics would be described by a wavefunction φ(

Since the usual quantum interpretation is p = hk, E = hω, the first thought was that these states represented negative energy solutions. But the difficulty with this was quickly realized: any interaction would cause positive energy solutions to decay into negative energy ones, and consequently normal states including the vacuum state would be unstable.

So Dirac proposed his 'hole theory', in which the negative energy levels are fully occupied. The Pauli principle would prevent the transition of any more particles to those levels. In this theory the positron was seen as an unoccupied negative energy level. But hole theory is wrong. In the first place it only works for fermions. In the second place the fully occupied sea would result in the vacuum having infinite energy and infinite charge, with real physical consequences which are not observed.

Feynman's idea of positrons moving backwards in time was next, and while this, along with his diagram expansion, made his calculations much easier, it is wrong also.

Here's what we now understand. Relativistic quantum theory is not described by a wavefunction analogous to the Schrodinger wavefunction. The quantity φ(

- #3

prajor

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BTW, may I know if there is a comprehensive source (book / site) covering other areas, leading to the current understanding as you explained ?

- #4

Dickfore

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A Feynmann diagram is a visual representation of particle interactions in quantum field theory. It uses lines and vertices to show how particles interact with each other.

In a Feynmann diagram, a positron is represented by an arrow pointing backwards in time. This convention was introduced by Richard Feynmann, who used it to represent the antiparticle of the electron.

Feynmann diagrams are important because they provide a way to visualize and calculate the probability of particle interactions. They are also used in theoretical calculations to understand the behavior of particles in different physical situations.

In experiments, Feynmann diagrams are used to interpret and analyze the results of particle collisions. By comparing the predicted diagrams with the actual data, scientists can validate or refine their theories about particle interactions.

While Feynmann diagrams are a useful tool, they also have limitations. They only represent a limited number of possible interactions and do not take into account quantum effects such as virtual particles. Additionally, they cannot fully describe interactions involving strong nuclear forces, which require more complex diagrams.

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