Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
When to Use this Tag
quantum-field-theory 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 condensed-matter or particle-physics, depending on your background. As QFT allows for a Lorentz-invarint formulation of quantum mechanics, general-relativity and special-relativity go well with quantum-field-theory. If your question is about QFT in a curved background, you should use qft-in-curved-spacetime.
Some major topics in QFT are renormalization, feynman-diagrams, gauge-theory, path-integral, supersymmetry, symmetry-breaking, scattering, etc. Use these tags (or any other one that is relevant to your question) together with quantum-field-theory to increase the chances for experts in a particular topic to see your post.
Avoid tagging a question as both quantum-field-theory and quantum-mechanics, the same is true for lagrangian-mechanics and hamiltonian-mechanics, 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 quantum-field-theory. 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 general-relativity. Questions concerning the quantum mechanical aspects of gravity should be tagged with quantum-gravity.
One of the major needs for theories like string-theory 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 standard-model are worked out pertubatively. You may use non-perturbative to tag questions that are about the non-perturbative aspects of QFT.
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.
