A rigorous treatment of entanglement entropy in quantum field theory: reduced density matrices, replica trick, area law, entanglement entropy in conformal field theory, the Ryu-Takayanagi formula, and the role of entanglement in quantum gravity.
A detailed exposition of BRST symmetry, its cohomological structure, and applications to perturbative and non‑perturbative gauge‑theory quantization.
An in-depth exploration of the AdS/CFT correspondence, its derivations, implications for quantum gravity, and connections to black hole thermodynamics and operator algebras.
A rigorous treatment of supersymmetry: the graded Lie algebra, supermultiplets, superspace and superfields, the Wess-Zumino model, softly broken supersymmetry, the Minimal Supersymmetric Standard Model, gauge coupling unification, and the role of SUSY in string theory and the search for a Theory of Everything.
A rigorous treatment of conformal field theory: the conformal group, primary operators, operator product expansion, radial quantization, conformal bootstrap, minimal models, and the space of conformal theories.
A rigorous treatment of black hole thermodynamics: the four laws, Hawking radiation via Bogoliubov transformation, Bekenstein-Hawking entropy, the information paradox, Page curve, replica wormholes, and implications for a theory of quantum gravity.
A rigorous treatment of topology and geometry in physics: fiber bundles, characteristic classes, Berry phase and Chern numbers, instantons, anomalies, index theorems, and the role of global structure in unification.
A rigorous treatment of modern cosmology: FRW geometry, Friedmann equations, inflation as an effective theory, cosmological perturbation theory, the cosmic microwave background, and the connections between early-universe physics and fundamental theory.
A rigorous analysis of the fundamental obstacles to quantizing gravity: perturbative non-renormalizability, background independence, the problem of time, black hole thermodynamics, and the conceptual foundations of candidate approaches.
A rigorous treatment of effective field theory: Wilsonian decoupling, operator expansions, power counting, matching, symmetry constraints, naturalness, and the layered structure of physical law.