Titlebook: Quantum Field Theory; An Introduction Gordon Walter Semenoff Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive

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Prologue,ork. Also, having gone through the trouble of reformulating a quantum system in the language of quantum field theory, we will learn how to extract some information about the physical systems that we are studying from the quantum field theory itself.

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Many Particle Physics as a Quantum Field Theory,system with many identical particles. For now, we will assume that the particles are non-relativistic in that their velocities are much less than the speed of light. The generalization to relativistic particles and relativistic quantum field theory will be discussed in later chapters. We will assume

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Degenerate Fermi and Bose Gases, previous chapter in the limit where the volume is very large, the density is finite and the inter-particle interactions are weak. This will introduce the idea of Fermi energy and Fermi surface for fermions, the concept of particles and holes, and it will allow us to study some of the properties of

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,Non-relativistic Space–Time Symmetries,how to extract the equations of motion and the equal-time commutation relations from knowledge of the Lagrangian density. Then we studied one of the great advantages of the action formalism and describing the field theory using a Lagrangian density. This advantage is the existence of Noether’s theor

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Photons,is responsible for electromagnetic interactions, is an example of such a field. It, together with the Dirac field which we studied in the previous chapter, comprise the fields of quantum electrodynamics which will an example of an interacting quantum field theory that will be of interest to us.

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Functional Methods,ey do not interact with other fields. In order to proceed further, it will be convenient to, once again, repackage the information that is contained in either the Lagrangian density or the field equations and equal-time commutation relations of a quantum field theory in a third form, the set of all