From Fields to Emergent Collective Physics
A compact collection of lecture notes on quantum many-body theory: quantum-mechanical and spin path integrals, field formulations and response functions, collective modes and Fermi-liquid theory, BCS superconductivity, neutral superfluids, and renormalization-group methods.
Lecture Notes
Path Integrals in Quantum Mechanics
Introduction to the path-integral formulation of quantum mechanics: amplitudes as sums over histories, the action principle, imaginary-time methods, and the bridge from operator quantum mechanics to functional integration.
Open PDFSpin Path Integrals & the Theta Term
Path-integral formulation for quantum spins, including spin coherent states, Berry-phase structure, continuum descriptions, and the appearance and physical role of the topological theta term.
Open PDFPath Integrals & Fields
Path-integral formulation of quantum many-body systems and the introduction of field variables as the foundation for diagrammatic and effective-field-theory methods.
Open PDFOperator Formalism & Response
Operator methods for interacting many-body systems together with response-function techniques describing how a quantum system reacts to external perturbations.
Open PDFRPA, Plasmons & Ferromagnetic Spin Waves
Random-phase approximation and collective excitations in interacting systems, including density oscillations, plasmons, and ferromagnetic spin-wave modes.
Open PDFLifetime & Correlation Energy
Interaction effects beyond the simplest mean-field picture, with emphasis on quasiparticle lifetime, decay processes, and many-body correlation energy.
Open PDFFermi Liquid Theory
Landau's low-energy description of interacting fermions: quasiparticles, phenomenological interaction parameters, and the organization of physics near the Fermi surface.
Open PDFBCS Theory & Charged Superfluids
BCS pairing and the physics of charged superfluids, connecting microscopic Cooper pairing with collective electromagnetic response.
Open PDFNeutral Superfluids
Neutral-superfluid physics and its low-energy collective behavior, providing a complementary perspective to charged condensates and superconductors.
Open PDFRG, Nonlinear Sigma Model & Kosterlitz–Thouless Physics
Renormalization-group ideas, nonlinear sigma models, and Kosterlitz–Thouless physics as long-wavelength tools for interacting, ordered, and topological systems.
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