What roll does government play in capitalism

In capitalism, the government acts as an 'invisible hand' like Adam Smith, a capitalist advocated says. Basically, the government stays out of ALL economic affairs in capitalism, instead they provide institutions such as schools and roads for their people. A capitalist economy is run by the people, not by the government.

The proper role of government in a capitalist economic system has been hotly debated for centuries. Unlike socialism, communism or fascism, capitalism does not assume a role for a coercive, centralized public authority.