Models
A quantum field theory becomes concrete when its fields, interactions, symmetries, and observables are specified. Explore named theories here: what defines them, which phenomena they explain, what can be calculated, and where their descriptions apply. Each profile develops a useful calculation and connects it to fuller treatments in the Library.
Find a model for your question
Section titled “Find a model for your question”| Chapter | What you can explore |
|---|---|
| Free Fields | How particles, antiparticles, spin, and gauge constraints appear before interactions are introduced. |
| Scalar and Fermion Interactions | How local interactions produce scattering, change vacuum structure, and connect to critical behavior. |
| Gauge Theories | How charged matter and gauge-field self-interactions lead to different behavior at short and long distances. |
| Lower-Dimensional Models | How simpler settings reveal mass generation, screening, solitons, and geometric interactions. |
| Conformal and Topological Models | How scaling dimensions, fusion, winding, and braiding characterize theories beyond ordinary particle scattering. |
| Supersymmetric Models | How symmetry relates bosons and fermions and constrains vacua and quantum dynamics. |
| Quantum Matter and Effective Theories | How microscopic Hamiltonians and low-energy descriptions organize many-particle systems and their controlled approximations. |
For a first example, start with the Real Scalar Field and then Scalar φ⁴ Theory to see what an interaction changes. For a familiar physical theory, enter through Quantum Electrodynamics. You can also open any chapter directly; the profiles explain the defining ingredients before using them.
Compare theories carefully
Section titled “Compare theories carefully”Compare the same properties: spacetime dimension, degrees of freedom, symmetries, parameters, observables, and the regime in which a result is controlled. An action is a starting point. A quantum theory can also require a regulator and its limiting prescription, a choice of state, boundary conditions, and global information about its fields or gauge group.
The chapters provide convenient entry points, and their subjects overlap. The compact free boson is both free and conformal; supersymmetric Yang–Mills theories are also gauge theories. A microscopic lattice model, its continuum limit, and a critical conformal theory are related descriptions with different defining data. The profiles keep those distinctions explicit.
This selection contains twenty-four profiles. It is a starting collection rather than an exhaustive classification of QFT. Use the Library menu or site search for other theories and for longer derivations. Reference supplies definitions, formulas, and conventions; Research examines current questions and the evidence behind proposed answers.