Which words are pronounced with an /ɑː/ or /æ/ depending on dialect?

Question

Certain English words are pronounced with two different vowels depending on the dialect of the speaker, namely with /ɑː/ or /æ/ (in IPA notation). These include:

can't, last, fast, past, path, vast, dance

Can you point me to a list of all common words with this property?

I recently heard the word “path” in a sound recording pronounced as /pæθ/, and didn't recognize it despite repeatedly listening. I was aware that “can't” has two pronunciations, but I didn't know this about all these words. I am asking this question so that in the future I have less trouble understanding such words.

Update: for search, here is a list of some such words that may be similar, based on the answer: advance, advantage, after, answer, ask, aunt, branch, brass, can't, cast, castle, chance, class, command, contrast, dance, demand, disaster, draft, enhance, example, fast, glass, glance, grant, graph, grass, half, last, laugh, mask, master, nasty, pass, past, path, photograph, plant, rather, sample, shan't, staff, task, vast.

Answer 1

What you are hearing is the infamous trap–bath split.

Some accents (like GenAmE) do not distinguish the vowels in trap and bath (both /æ/). But many BrE (RP and mainstream) and Oceanic (AusE, NZE, SAE) make a distinction. In contexts before /f, s, θ, ns, nt, ntʃ, mpl/, the /æ/ changes to /ɑː/.

So it depends on which country you’re in. Trap sounds mostly the same in AmE and BrE, but bath sounds ‘Englishy’ in BrE to Americans (and vice versa to the English).

The Wikipedia article on the phonological history of English short ‘a’ and in particular its trap–bath split article give the rule, lots of examples, and the many exceptions.