Effective-Theory Architecture Atlas
An effective theory should be chosen from the physical problem, not from a familiar acronym. Start with the observable and state, identify the active degrees of freedom and scale hierarchy, specify how symmetries act, and only then choose the power counting, matching data, and uncertainty model. This chapter is organized around that decision: a common architecture map comes first, followed by bounded cards for Goldstone, few-body, heavy-particle, nonrelativistic, electroweak, gravitational, hydrodynamic, and open-system theories.
Enter this chapter
Section titled “Enter this chapter”Begin with A Map of Effective-Theory Architectures to choose an effective description from the observable and its hierarchy.
Topics
Section titled “Topics”- A Map of Effective-Theory Architectures — Compares active fields, symmetry realization, and expansion parameters.
- Chiral Effective Theory and Nonlinear Symmetry — Organizes Goldstone interactions by derivatives and explicit breaking.
- Nuclear and Few-Body EFT Architecture — Includes shallow poles and the resulting few-body counting.
- Heavy-Particle EFT and HQET Architecture — Separates heavy rest mass from a single particle’s residual motion.
- NRQED, NRQCD, and Potential EFT Architecture — Resolves the momentum and binding-energy scales of slow heavy pairs.
- SMEFT and HEFT: Architecture and Domain — Distinguishes linear and nonlinear electroweak symmetry realizations.
- Effective Field Theory of Gravity: Architecture and Power Counting — Organizes low-energy gravitational corrections by symmetry and derivatives.
- Hydrodynamic Effective-Theory Architecture — Expands the dynamics of conserved quantities and other slow modes.
- Open-System Effective-Theory Architecture and Consistency Conditions — States when removing an environment permits a controlled reduced description.
How the ideas fit together
Section titled “How the ideas fit together”The same particle label does not select the same expansion. A heavy-light system can retain one heavy source with small residual momentum, whereas a slow heavy pair introduces separate momentum and kinetic-energy scales. Similarly, an environmental degree of freedom may generate memory rather than an instantaneous local interaction when removed. The hierarchy and the observable decide which effects must remain explicit. Architecture selection therefore precedes power counting, matching, and numerical fitting. Manohar 2018, §§ 3.1–3.3.
Where to go next
Section titled “Where to go next”Continue to Naturalness, Scale Sensitivity, and Emergence to separate a calculable threshold correction from its interpretation.