These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's $c$ -theorem, Wess-Zumino-Witten models, modular invariant partition functions, and the connections to entanglement entropy. The material presented is based on lectures at the Southeast University Summer School and the course at Fudan University.These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's $c$-theorem, Wess-Zumino-Witten models, modular invariant partition functions, and the connections to entanglement entropy. The material presented is based on lectures at the Southeast University Summer School and the course at Fudan University.

arXiv:2208.05180Aug 10, 20220 citations

The Self-Consistent-Field Method in Nuclear Theory

R.V. Dzholos, В.Г. Соловьев

Springer eBooksJan 1, 19720 citations

On the Reduction Structure of Effective Theories

Masaru Moriyama

This technical note compares the Q-box formalism of nuclear physics with density functional theory (DFT) of quantum chemistry and condensed matter physics, from a renormalization group (RG) perspective. Although the two theories developed independently, both share the methodological philosophy of eliminating intractable degrees of freedom to obtain a lower-dimensional effective description. This note formalizes that intuition, arguing that both belong to a Shared Methodological Lineage rooted in Wilsonian effective theory and stand in a Structural Analogy, traversing symmetric yet distinct paths in reduction axis and mathematical foundation. Key contents:- Formal juxtaposition of reduction operations: energy-scale reduction (Q-box) vs. spatial-dimension reduction (DFT)- Unified abstract structure as reduction maps R : X -> Y, with explicit asymmetry between R_Q (non-invertible, approximation-dependent) and R_D (invertible in principle via the Hohenberg-Kohn theorem)- Mathematical depth of DFT: Levy constrained search, Legendre transform isomorphism with the 1PI effective action, existence and unknowability of the universal functional- Genealogical comparison with Wilson RG, SRG (Wegner 1994; Glazek-Wilson 1993), DMRG (White 1992), and the 1PI effective actionThis technical note compares the Q-box formalism of nuclear physics with density functional theory (DFT) of quantum chemistry and condensed matter physics, from a renormalization group (RG) perspective. Although the two theories developed independently, both share the methodological philosophy of eliminating intractable degrees of freedom to obtain a lower-dimensional effective description. This note formalizes that intuition, arguing that both belong to a Shared Methodological Lineage rooted in Wilsonian effective theory and stand in a Structural Analogy, traversing symmetric yet distinct paths in reduction axis and mathematical foundation. Key contents:- Formal juxtaposition of reduction operations: energy-scale reduction (Q-box) vs. spatial-dimension reduction (DFT)- Unified abstract structure as reduction maps R : X -> Y, with explicit asymmetry between R_Q (non-invertible, approximation-dependent) and R_D (invertible in principle via the Hohenberg-Kohn theorem)- Mathematical depth of DFT: Levy constrained search, Legendre transform isomorphism with the 1PI effective action, existence and unknowability of the universal functional- Genealogical comparison with Wilson RG, SRG (Wegner 1994; Glazek-Wilson 1993), DMRG (White 1992), and the 1PI effective action

May 21, 20260 citations

These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's

c

-theorem, Wess-Zumino-Witten models, modular invariant partition functions, and the connections to entanglement entropy. The material presented is based on lectures at the Southeast University Summer School and the course at Fudan University.