The United States of America was a formally independent federal constitutional republic consisting of 48 states, a federal district, and various territories situated in North America and abroad.
Following the invasion of the Greater Nazi Reich and Japanese Empire in 1945, and subsequent nuclear bombing of Washington, D.C., the United States collapsed and was divided by its conquerors into three separate territories - Nazi America in the east, the Japanese Pacific States in the west, and the Neutral Zone acting as a slim buffer between the two.
The United States of America was a thriving, powerful nation with a stable government until the Stock Market Crash of 1929, where the United States entered the Great Depression, experiencing high unemployment and a declining economy. The history of the United States diverged in 1933, when President Franklin Delano Roosevelt was assassinated. With Roosevelt not having a chance to enact the New Deal, the Great Depression persisted in the U.S. well into 1940s, along with its policy of isolationism. As a result, the United States was both unwilling and unable to assist the Allies against German aggression when World War II broke out in 1939. By this time, the United States was only surpassed in power by the combined British Empire, making it the second most powerful nation on the planet.
The United States was drawn into the war when the Japanese bombed Pearl Harbor in December 1941. The attack was devastating; not only was the United States Pacific Fleet entirely destroyed, but Japan successfully invaded and occupied Hawaii in the immediate aftermath. The United States recaptured Hawaii in February 1942, providing a welcome morale boost, but this victory was short-lived and Hawaii was eventually lost again.
After the collapse and capitulation of the United Kingdom and Soviet Union, Nazi Germany and Japan launched a frontal assault on both coasts of the U.S. in 1945. As the most of the world had already fallen, the United States was left to face both of its enemies alone. Despite heavy losses, the Americans managed to hold out against the initial Axis attacks.
Then, at some point during the invasion, the Germans decided to deploy the newly-created Heisenberg Device, an atomic bomb. It was dropped on Washington D.C. on December 11, 1945. The bomb utterly destroyed the city, resulting in the collapse of the United States Government and the senior military leadership. Although what was left of the government surrendered, remnants of the military as well as citizens fought hard to prevent an Axis takeover of the country. The American Resistance fought a tenacious war against both Germany and Japan for almost two years, but ultimately succumbed to the Axis Powers. On September 18, 1947, Victory over America was declared, and the full surrender of the United States was achieved. The United States was divided into three zones: the Japanese Pacific States in the west, Nazi America in the East, and a slim buffer zone, the Neutral Zone, in between.
In 1947, Adolf Hitler announced that the Axis Powers had eliminated all members of the Resistance and that America had at last fallen and been conquered. Ever since the war, there has been bitter resentment between the Axis Powers and the former United States residents.
After "traveling" via meditation to an alternate timeline, Nobusuke Tagomi witnessed a United States where the Allies had won World War II. The country was never invaded and divided. In this alternate 1962, the United States was engaged in a Cold War with its former war ally, the Soviet Union, and both countries were close to armed hostilities due to their involvement in the Cuban Missile Crisis.
Unlike in Nazi America, the capital of the United States remained Washington D.C. and the President of the United States was John F. Kennedy (as evident on the front page of a newspaper Tagomi saw on a bench in San Francisco's Union Square). The flag of the United States in this "alternate" 1962 has 50 stars in the blue field (denoting that Alaska and Hawaii were made official states of the USA).