Is it okay to omit the space after a comma in square bracket references, e.g. "[45,46,47,64]" in a research paper
This is strictly a style manual question.
Check with the publisher of your paper. If it's a university (your MS thesis or PhD dissertation), you'll have to follow the university's style rules. If it's an academic journal, it'll either dictate a standard style manual, like the CBE or APA, or else the publisher's style manual. You'll have to follow the style manual's rules, not your gut or anyone else's advice, about this.