Undergrad Is this a new theory, an enhanced theory or just philosophy?

[Auto-Didact]

But none of the above authors mention anywhere that $f(t,x)$ and $g(t,x)$ would represent two different kinds of particles...

 

[A. Neumaier]

It's utter nonsense to begin with. There's no "photon wave function" to begin with, because there's no position representation for photon states, because there's no photon position operator definable.

I am no expert in the field but many papers like following seem to be genuine physics.
https://www.sciencedirect.com/science/article/pii/S0003491616300173

Bialynicki-Birula is definitely a serious theoretician who has a long record of multiple insightful works; I have read some of his work in the past. If one is willing to disparage his work as 'nonsense' then I believe practically no theorist is safe from criticism.

The confusion is explained by the fact that the term ''wave function'' is ambiguous.

If the term is reserved for the position representation with Born's probability interpretation then vanhees71 is right. But there is a wave function in the momentum representation with a proper probability interpretation, and Bialynicki-Birula discusses its Fourier transform, which also deserves the name ''wave function''. Though it doesn't have a probability interpretation it completely describes the state.