Quantum Field Theory was developed as the theory unifying Quantum Mechanics and Relativistic Field Theory for the purpose of describing physics of elementary particles. Quantum Electrodynamics, electro-weak theory, Quantum Chromodynamics and the Standard Model of elementary particles are all particular examples of Quantum Field Theory, which had great success in high-energy physics. At the same time, it was realized that a straightforward application of Quantum Field Theory to Einstein gravity does not give a physically sensible quantum gravity theory because of its nonrenormalizability.

More recent applications of Quantum Field Theory are no longer limited to physics of elementary particles. They also include many successful applications to nuclear physics, condensed matter physics and pure mathematics. At the same time, the formalism of Quantum Field Theory has to be further developed because of the new challenges, such as quantum gravity and quantization with higher derivatives, strong coupling and bound states, computational techniques in quantum perturbation theory, and more rigorous mathematical foundations.

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