Quantum Field Theory

Relativistic quantum theory of fields underlying particle physics and condensed matter.


foundation tier

Quantum Field Theory is a topic within modern and quantum. Relativistic quantum theory of fields underlying particle physics and condensed matter. The area sits at the intersection of foundational theory and active research practice, and its methodology is shaped by a small set of canonical references that frame how problems are posed, how results are validated, and what counts as progress.

Work in this area progresses along several axes: the canonical theoretical framework, benchmark problems that calibrate methods against known answers, computational and experimental tooling that extends reach to larger or more complex systems, and frontier questions that current references either open up or partially answer. The references cited below illustrate these axes in different ways and together define the working vocabulary of the field.

Foundational references

The primary references for this topic establish the conceptual core and the standard problem set.

An Introduction to Quantum Field Theory (Peskin et al., 1995) is treated here as a primary reference for this area; its presentation of the subject is the canonical entry point for learners moving from prerequisites into independent work on quantum field theory.

The Quantum Theory of Fields, Volume I (Weinberg, 1995) is treated here as a primary reference for this area; its presentation of the subject is the canonical entry point for learners moving from prerequisites into independent work on quantum field theory.

Open methodological questions in quantum field theory include the precise scope of validity of the current dominant techniques, the integration of newer computational or experimental tools, and how this topic connects to neighbouring areas in the tree. Subsequent waves of editing will deepen these connections and add fresh frontier references as the literature evolves.

Prerequisites

Sources

  • textbook · primary · 1995
    An Introduction to Quantum Field Theory
    peskin-1995, schroeder-1995
  • textbook · primary · 1995
    The Quantum Theory of Fields, Volume I
    weinberg-1995

In context

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  1. 01

    Canonical Quantization

    Operator quantization of free fields and equal-time commutation relations.

  2. 02

    Path Integral Quantization

    Functional integrals, generating functionals, and gauge fixing for quantum fields.

  3. 03

    Renormalization and the Renormalization Group

    Cutoffs, counterterms, beta functions, and Wilsonian flow of effective couplings.

  4. 04

    Gauge Theory

    Yang–Mills fields, Faddeev–Popov ghosts, and BRST quantization.

  5. 05

    Effective Field Theory

    Systematic low-energy expansions matching microscopic theories to symmetry-based effective Lagrangians.

  6. 06

    Conformal Field Theory

    Scale-invariant quantum field theories underlying critical phenomena and string worldsheets.

  7. 07

    Supersymmetric Field Theories

    Field theories with fermion–boson symmetry, holomorphy, and non-renormalization theorems.

  8. 08

    Topological Field Theory

    Metric-independent QFTs producing topological invariants of manifolds.

  9. 09

    Anomalies in QFT

    Chiral, gauge, and gravitational anomalies and their cancellation in consistent theories.

  10. 10

    Quantum Field Theory in Curved Spacetime

    Fields on classical curved backgrounds, particle creation, and the Unruh and Hawking effects.

  11. 11

    Lattice Field Theory Methods

    Discretized formulations of QFT, Monte Carlo evaluation, and the continuum limit.

  12. 12

    Non-Perturbative QFT

    Instantons, solitons, dualities, and non-perturbative phenomena beyond Feynman expansions.

  13. 13

    Scattering Amplitudes

    On-shell and recursive methods, generalized unitarity, and amplitudes beyond Feynman diagrams.

  14. 14

    Finite-Temperature Field Theory

    Imaginary-time formalism and thermal QFT for cosmology and many-body physics.

  15. 15

    Non-Equilibrium Field Theory

    Keldysh and closed-time-path techniques for quantum systems out of equilibrium.

  16. 16

    Generalized Symmetries

    Higher-form, non-invertible, and categorical symmetries in modern QFT.

  17. 17

    Integrable Field Theories

    1+1 dimensional QFTs with infinite conserved charges and exact S-matrices.


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