Joanna Kulig’s work in “Cold War” is one of those rare cases, like Keisha Castle-Hughes in “Whale Rider” or Giulietta Masina in “Nights of Cabiria,” where the movie seems to have found literally the one person in the world who could play the part.

The Polish actor has done lots of stuff — she was in “Cold War” director/co-writer Pawel Pawlikowski’s last movie, the Oscar-winning “Ida” — but her performance as Zula is so powerful and erotic and nuts that it doesn’t feel like a performance at all. If Kulig, who resembles Jessica Chastain, were American, Hollywood would be offering her everything.

It’s like Europe is the world’s smallest town in “Cold War,” which is on this year’s foreign film Oscar shortlist. The movie skips from one capital to another over 15 years, showing us Zula and Wiktor (Tomasz Kot) bumping into each other again and again in a relationship so passionate but upsetting that it feels like the only thing more dangerous than them being apart is them being together.

Because Pawlikowski has structured “Cold War” as a series of white-hot highlights in the couple’s romance, without much connecting material, my a-few-weeks-after-seeing-it version of the movie is that it’s basically a series of moments in which Zula does amazing things and Wiktor is overwhelmed by them.

Both characters are musicians (she’s a folk singer, he plays jazz piano), and one touchstone of the movie is the power of music to alter our moods. This is best demonstrated in a scene where they’re in a bar after one of their more than a dozen fights and suddenly “Rock Around the Clock” comes on. No one ever says it — the movie isn’t big on giving us context for anything — but it sure seems like this is the first time Zula has ever heard rock music, and she responds with mad, orgiastic dancing that draws others into her ecstasy.

What’s the movie about? Who cares? “Cold War” is focused on sensation and feeling, not plot, which is almost certainly a deliberate choice of Pawlikowski’s, who dedicates the movie to his parents and has said it was inspired by their relationship. The movie doesn’t pretend to understand what it is that attracts and repels its characters and, honestly, who would say they understand their own parents’ love story?

My take is that it depicts its female lead as impetuous and unknowable because its male lead is so wrapped up in his own image of her that he never bothers to figure out how she views the world. (In the opening scenes, Wiktor is told that Zula killed her father, which turns out not to be true but which seems to forever define her as dangerous goods.) It’s possible that the movie’s point is that this relationship grows toxic because Wiktor will cross borders, tell lies and go to prison for Zula, but he can’t get out of his own head.

Or maybe the point is that Pawlikowski is drunk on movie love. He makes two bold visual choices in “Cold War,” filming it in black-and-white and using a frame that is almost square rather than the traditional wide rectangle. Both will remind movie fans of midcentury foreign films in which artists such as Jean-Luc Godard and Federico Fellini gave us tales of mad, inexplicable love like “Breathless” and “La Dolce Vita.”

Maybe what “Cold War” is really about is the movies. Maybe Pawlikowski, bewildered by his parents’ love, is trying to figure it out the only way he knows how: via the movie classics that were made in the very years his parents were falling in and out of love.