Problem with derivation of phase for 1-fermion state

In summary, The conversation is about a problem with the (-1) term in the spherical-vector method for helicity amplitudes. The individual believes there may be a mistake in the substitution and suggests a possible correction.
  • #1
ChrisVer
Gold Member
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Take a look at the attachment, my question is obvious from the colored points. The attachment is from:
"state-of-the-art formulas for helicity amplitude calculation and all that
(version 2.4)
PART Ia. Spherical-Vector Method for Helicity Amplitudes
(FORMALISM)
Ken-ichi Hikasa"

I think there is a problem with the [itex](-1)[/itex] term. If

[itex]u^{1}_{h}(p)= (-1)^{h-\frac{1}{2}} e^{2ih \bar{\phi}} u^{2}_{h}(p)[/itex]

Then I think when he did the substitution to my underlined step there should be a:

[itex](-1)^{\frac{1}{2}-h} [/itex] instead... At first I thought I had derived wrong the particle 1-2 spinors relation, but my idea is also boosted from the fact he changes the sign of the exponential.

The same is also true for the antiparticle spinor [itex]v[/itex] (blue)
 

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  • #2
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 

1. What is the problem with the derivation of phase for 1-fermion state?

The problem with the derivation of phase for 1-fermion state arises from the fact that fermions are particles with half-integer spin, such as electrons, protons, and neutrons. According to the laws of quantum mechanics, the phase of a fermion state is not well-defined and cannot be measured directly.

2. Why is the phase of a 1-fermion state not well-defined?

This is due to the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. As a result, the phase of a fermion state is not a measurable quantity and can vary depending on the measurement process.

3. How do scientists try to overcome this problem?

One approach is to use the concept of gauge invariance, which is a mathematical property that ensures the physical predictions remain unchanged even if the phase of a fermion state is altered. This allows scientists to work around the issue of not being able to directly measure the phase of a 1-fermion state.

4. Are there any proposed solutions to this problem?

There have been various proposed solutions to this problem, such as using entanglement and interference effects to indirectly measure the phase of a fermion state. However, these solutions are still under development and require further experimentation and validation.

5. Why is it important to understand the phase of a 1-fermion state?

The phase of a fermion state is a fundamental concept in quantum mechanics and is essential for understanding the behavior and properties of fermions. It also has practical applications in fields such as quantum computing and materials science, making it crucial for further research and development in these areas.

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