Spin 2, what wavefunction?

[Enthalpy]

Hello you all!

 

For an electromagnetic wave (spin=1) we write the wavefunction as a vector (or little more), depending on position and time.

 

For an electron (spin=1/2), as a scalar (though the angular momentum is treated separately then).

 

What mathematical object shall represent a particle with spin=2?

 

Thank you!

[swansont]

Photons behave somewhat differently because they're massless, not necessarily because they are spin 1

[Enthalpy]

Photons behave somewhat differently because they're massless, not necessarily because they are spin 1

 

Yes, speed=c removes the possibility that the electric field is parallel to the propagation. Massive particles with spin=1 could be polarized horizontally, vertically or along speed.

 

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We use to write the wavefunction of photons as

Electricfield (position, time)

because it preexisted QM, is more explicit, and is more convenient to deduce the properties.

 

Though, QM has a uniform formulation, applicable to photons as well:

Psi (polarization, position, time)

and then Psi is just the complex function used for other particles.

 

Instead of telling "the electric field is that vector" it answers "your guess is probable". The guess to detect the photon there, then, with that polarization - with the chances to detect a photon related with the electric field intensity.

 

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The formulation as Psi (polarization etc) is often less convenient but it fits entangled photons more naturally.

 

Remember the two spin-entangled photons which can be linearly or circularly polarized:

• If one is detected horizontal, the other as well (with probabilities). If vertical, the other as well.
• From the same source, if one is detected right, the other as well. If left, the other as well.

 

If writing each photon wavefunction as Electricfield (position, time) one has to choose between

• Linear electric fields. A phased sum synthesizes a circular field where needed, but this sum must be decided upon detection.
• Circular fields. The phased sum if detecting linearly must be decided upon detection.

I'm not so pleased with a weighted sum of wavefunctions whose coefficients are random. That is, a unique

Electricfield (position, time)

wavefunction does not describe the particle and can be written only upon detection.

 

As opposed, the wavefunction for both photons A and B

Psi (polarization A, position A, polarization B, position B, time)

can be fully written before knowing the random outcome.

 

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So, the wavefunction for a particle with spin=2 must just be

Psi (PolarizationMeaningfulWithSpinTwo, position, time)

and my initial quest would rather be re-written like:

 

"can we use some mathematical object, as we use a vector for the electric field of a single photon, to represent a single particle with spin=2, more conveniently than the wavefunction does?"