There Is a Way to Comprise Half-Integer Eigenvalues for Photon Spin

Institute of Physical Science and Engineering Tongji University, 200092, Shanghai, China Corresponding email: shaoxu-ren@hotmail.com Received 13 July; Accepted 25 July; Published 28 July ———————————————————————————————————– ———————————————————————————————————– Abstract In this article, an attempt based on Spin Topological Space, STS, to give a reasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in quantum mechanics, which can be used to account for where the unconventional half-integer spin eigenvalues phenomenon of light photon comes from. We suggest to dectect the possible existence of photonic one-third-spinization phenomenon of light photon, by using three beams of light photon in interference experiment.

This present article, " There is a way to comprise half-integer eigenvalues for photon spin ", is in the frame of Spin Topological Space, STS [2] to consider the contributions of spin effects of light photon, and tries to clear up the cause of the photonic fermionization phenomena, which emerged from the experiment [1].
The contributions of orbital effects of light photon, which show half-integer eigenvalues, could appeal to the mechanism of Non-Hermitian orbital angular momentum L 3 , L 2 [3].
Normally, in quantum mechanics, different kinds of spin particles possess different dimensional spaces, which are expressed by finite dimensional matrices, and these finite dimensional matrices are all Hermiticity.
Subscripts " 2 " and " -2 " represent the second minor top-right diagonal and the second minor down-left diagonal.
Subscripts " 0 " indicates major diagonal, sometimes for convenience be omitted.
In condition for keeping photon's Casimir operator invariant, that is, keeping Further, next three groups of math series forms of the spin third component  3 l of light photon are obtained as below Integer eigenvalues series form (20) and half-integer eigenvalues series form (21) give the accounts of " One family includes have the expected bosonic spectrum with integer eigenvalues, and other family, has a fermionic spectrum, comprising half-integer eigenvalues." (quoted passage from the paper [1]).

Physical behavior mechanism of photonic fermionization of light photon experiment
Now, matrices (8), ( 9), ( 10) can be used to describe the experiment rusults ( 17) and ( 19), ( 20), ( 21) of photonic fermionization phenomena of light photon, but from what kind of experimental procedure of physical behavior mechanism, these experimental results arise ?
For this reason, deeper research is given.Be concise, the sign of "( 1)", is omitted in follows.
BP and FP alternately appear with m.
2) For a fixed term of the new spin angular momentum  3; m/2 2 , m/2 −1 , there are many options to choose from the general expression (29).

1 )
There exist two diffrent families of the third component of light photon： family BP: Bosonization of Photon, labelled by "  ", family FP: Fermionization of Photon, labelled by "  "