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covers the theoretical description of many-body systems (such as fermionic gases in condensed matter) and high-energy physics/particle physics, starting from a given Lagrangian or Hamiltonian. You might hence also/only want to tag your question as or , depending on your background. As QFT allows for a Lorentz-invarint formulation of quantum mechanics, and go well with .


Avoid tagging a question as both and , the same is true for and , which are meant for the classical mechanics application of these formalisms.

The quantum field theories most worked on are special relativistic, and are sometimes known as relativistic quantum field theories, although it is more common to simply call it as and use for the non-relativistic QFTs. Examples of Relativistic QFTs include the following:

The latter, the Standard Model of Particle Physics, describes all experimentally known fundamental interactions (bosonic fields) and fermionic fields, except for gravity, which is classically described by .

One of the major needs for theories like is precisely this shortcoming of the standard model. Other needs include the vastly large number of dimensionless constants, the need for renormalisation, etc.

Many Quantum Field Theories, including the are worked out petrubatively.

Contrary to a popular myth, quantum field theory can be formulated on a curved spacetime, but clearly, then, gravity would still, be classical.

Prerequisites to learn Quantum Field Theory:

Phys: Non-Relativistic Quantum Mechanics (and all its math-phys prerequisites); Analytical Mechanics; Special Relativity (SR); Classical Electrodynamics; Classical Field Theory; Lagrangian formalism and action principles; Dirac Equation; Grassmann Algebras and Berezin Integration; Continuum Mechanics.

Math: Variational Calculus; Lie Groups, Lie Algebras and their representation theory; Functional Analysis and Operator Theory: Maybe also: Spectral theory for unbounded operators; distribution theory.

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