Background: I obtained a PhD in Theoretical Physics/Mathematical Physics in 2015 and have been working as a post-doctoral researcher in various institutions since. In the past few years, I developed a strong interest in Linguistics which I have been self-studying in my free time for about a year (mostly syntax, semantics and pragmatics), including delivering introductory talks to a study group about what I learned. However, I feel limited in my self-studying by my research work in Physics-which doesn't satisfy me as much as it used to-and so I have been thinking in quitting Physics to start study Linguistics full-time, with the goal of getting a PhD in Linguistics.
Question: My question is, is it possible for me to "capitalize" on having a PhD degree in Physics to somehow get faster to my goal (PhD position in Linguistics) or should I start from scratch?
I guess there are two sub-questions:
At the study level: To what extent is it possible to transfer competency from Physics to Linguistics? (I tend to feel that having a strong mathematical background is beneficial when studying the most formal aspects, like formal languages, formal semantics, etc. but probably would be of no help whatsoever for more applied subfields).
At the pragmatic/academic level: Very concretely, would it be possible to join e.g. a Master program/graduate school in a Linguistics topic without producing a Bachelor degree/License in the same field? Are there some specific formations that accept students with wider backgrounds such as mine?