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The field of quantum plasmas has a long and diverse tradition and is becoming of increasing current interest, motivated by applications to micro-electronics and to focused high-power lasers. In this book, plasma kinetic theory is developed a covariant (4-tensor) notation, which facilitates generalizations to include all relativistic and electromagnetic effects. Relativistic quantum effects are incorporated by synthesizing the theory with quantum electrodynamics (QED), including the plasma responses in QED, and using QED to calculate the plasma response 4-tensors.