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Quantum field theory is a mathematical model used to describe the behavior of physical systems. It allows particles to interact and exchange momentum, and this allows for forces to arise. The theory is incomplete, as it cannot be unified with general relativity, which describes the behavior of gravitation.

**00:00:00**In this video, physicist Michael Nielsen introduces quantum field theory, which is a mathematical framework that reconciles the principles of quantum mechanics with the laws of classical physics. The theory allows for the description of the evolution of particles over time, but it fails to take into account the two considerations mentioned at the beginning of the video: that particles can disappear and that each particle exhibits the same properties within a family of particles. In order to build a more general description of the microscopic world that takes these limitations into account, Nielsen introduces a field into the equation. Each object in the field is represented by a mathematical object, and the field must obey the conservation of certain quantities over time in order to be consistent with the principles of relativity.**00:05:00**This video explains how quantum field theory can be used to visualize the behaviour of energy, momentum, angular momentum, and velocity of the centre of mass in a space-time filled with a quantum field. It also describes how fields with complex numbers exhibit an internal symmetry that implies the conservation of another quantity over time - in this case, the electric charge. Finally, the video explains how fields with various symmetries can be distinguished and how they give rise to particles with different charges and colours.**00:10:00**Quantum field theory is a mathematical model used to describe the behavior of physical systems. It allows particles to interact and exchange momentum, and this allows for forces to arise. The theory is incomplete, as it cannot be unified with general relativity, which describes the behavior of gravitation.**00:15:00**Quantum field theory is a theory of the universe that explains the behavior of particles and forces by taking into account the behavior of fields. In curved space times, some results of the theory can already be calculated. For example, scientists have predicted that black holes will evaporate over time. However, scientists are still looking for a unified theory that would explain microscopically why space-time gets curved and would reconcile the infinitely large with the infinitely small gravity with quantum theory.

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