“I held up my local convenience store to get a bus ticket,” Johnny says with a smirk as he and a pal head out of town.

“Actually I stole the money from my mom’s dresser.”

Beat.

“Actually she lent me the cash.”

Such is the sheepish fate of a would-be rebel today. But at least Johnny and his buddy Tunny (Stark Sands) do manage to escape deadly suburbia for the lively city, bringing along just their guitars and the anomie and apathy that are the bread and butter of teenage attitudinizing the world over. (“I don’t care if you don’t care,” a telling lyric, could be their motto.)

The friend they meant to bring along, Will (Michael Esper), was forced to stay home when he discovered that his girlfriend (Mary Faber) was pregnant. Lost and lonely, and far from ready for the responsibilities of fatherhood, he sinks into the couch, beer in one hand and bong in the other, as his friends set off for adventure.

Beneath the swagger of indifference, of course, are anxiety, fear and insecurity, which Mr. Gallagher, Mr. Esper and Mr. Sands transmit with aching clarity in the show’s more reflective songs, like the hit “Boulevard of Broken Dreams” or the lilting anthem “Are We the Waiting.” The city turns out to be just a bigger version of the place Johnny and Tunny left behind, a “land of make believe that don’t believe in me.” The boys discover that while a fractious 21st-century America may not offer any easy paths to fulfillment, the deeper problem is that they don’t know how to believe in themselves.

Image John Gallagher Jr., center, and Tony Vincent, upper right, in “American Idiot.” Credit... Sara Krulwich/The New York Times

Johnny strolls the lonely streets with his guitar, vaguely yearning for love and achievement. He eventually hooks up with a girl (a vivid Rebecca Naomi Jones) but falls more powerfully under the spell of an androgynous goth drug pusher, St. Jimmy, played with mesmerizing vitality and piercing vocalism by Tony Vincent. Tunny mostly stays in bed, clicker affixed to his right hand, dangerously susceptible to a pageant of propaganda about military heroism on the tube, set to the song “Favorite Son.” By the time the song’s over, he’s enlisted and off to Iraq.

In both plotting and its emotional palette, “American Idiot” is drawn in brash, primary-colored strokes, maybe too crudely for those looking for specifics of character rather than cultural archetypes. But operas  rock or classical  often trade in archetypes, and the actors flesh out their characters’ journeys through their heartfelt interpretations of the songs, with the help of Mr. Mayer’s poetic direction and the restless, convulsive choreography of Steven Hoggett (“Black Watch”), which exults in both the grace and the awkwardness of energy-generating young metabolisms.