Final answer:
The federal courts have authority to hear cases that involve federal questions, including issues related to the Constitution, federal laws, or treaties, as well as cases where the U.S. government is a party. The Supreme Court has original jurisdiction in certain diplomatic and state-involved cases but chiefly acts as an appellate court. Special federal courts address specific federal matters like trade and claims against the government.
Step-by-step explanation:
The federal courts may only hear cases that Congress has granted them authority over, particularly those cases that involve a "federal question". A federal question includes matters involving the Constitution, federal laws, or treaties. This authority also extends to cases where the United States government is a party. State cases are more likely to be heard by federal courts when they involve federal issues, which could range from criminal violations of federal law to civil rights violations protected by the Bill of Rights.
Moreover, appellate courts, including the Supreme Court, have jurisdiction to hear appeals based on the subject matter. For example, the Supreme Court has original jurisdiction in cases involving states as parties and diplomatic figures and appellate jurisdiction over cases concerning the Constitution and federal law. Special federal courts like the U.S. Court of International Trade and the U.S. Court of Federal Claims handle specific types of federal issues, including international trade laws and claims against the United States government, respectively.