This is the .tex file, displayed in a plain mode:
In my custom LaTeX-mode, it displays as (but it still saves as above):
And of course this is the compile result, as you could expect from the first screenshot figure:
The lisp code is shared. As usual for free shares, it is without warranty and try-outs are at your own risk. On the other hand, the modification on display is based on only font-lock-mode and compose-region. No dirty hacks. Thus should be safe.
https://github.com/tririver/wyTex
I also put some custom settings of auctex in the same file. They are not necessary. The only essential part is the function wyTex-key. This function is actually bi-directional alias. If you can input α, β, etc directly from keyboard instead of \alpha, \beta, etc, then directly input them and in saved file they will be saved as \alpha, \beta, etc and thus can compile using latex or pdflatex directly.
Here is the wyTex-key function:
Acknowledgment: Thank Francesco for answering my elisp question. And Thank +Xah for suggesting writing an own mode to learn elisp!(defun wyTex-key (utf8-char tex-command)(local-set-key utf8-char`(lambda () (interactive) (insert ,tex-command)))(font-lock-add-keywords'wyTex-mode `((,(concat "\\(\\" tex-command "\\)")(0 (progn (compose-region (match-beginning 1)(match-end 1) ,utf8-char)nil))))))