Vvedensky never abandoned the “star of nonsense” until the very end. His works become increasingly profound and complex over time—the “star of nonsense” deepens, but at the same time becomes clearer: the style and character of the work become so clear and transparent that I sense absurdity, illogicality, nonsense as my own, precisely my illogical, absurd existence; I no longer see their illogicality. On the contrary, logic, as Vvedensky shows me, is something completely alien to me, external; logic itself, Aristotle’s logic itself begins to seem absurd to me. But nonsense is not relative. It is an absolute reality—it is the Logos made flesh. This personal Logos itself is illogical, just as His incarnation is. But this nonsense has become an understanding of my existence. It is impossible to understand nonsense: understood nonsense is no longer nonsense. Nor is it possible to seek the meaning of nonsense; The meaning of nonsense is the same, if not greater, nonsense. The “star of nonsense” is that which cannot be heard with the ears, seen with the eyes, or understood with the mind.
In spring 2025, I took the class “Group theory II” (Lie groups and Lie algebras) by Prof. Yuxin Liu (刘玉鑫). Because of the retirement of a professor, the course schedule this year was adjusted, and this class, originally taught by Prof. Yinan Wang (王一男), was assigned to Prof. Yuxin Liu, who taught this class before 2020. To my opinion, Prof. Liu’s class seems to be better, because it has a broader context, explains everything clearly without involving complex mathematical concepts, and introduces physical applications (especially in nuclear theory) in detail.
Reference books
The main reference book is Prof. Yuxin Liu’s 《物理学家用李群李代数》(Lie groups and Lie algebras for physicists), and I found the book 《物理学中的群论（第二版）》(Group theory for physicists (second edition)) by 马中骐 (Zhongqi Ma) useful. Other references books include:
Barut and Raczka, Theory of Group Representations and Applications.
Hamermesh, Group theory and its application to physical problems.
Wybourne, Classical Groups for Physicists.
万哲先 (Zhexian Wan), 李代数 (Lie algebra).
Iachello, Lie Algebras and Applications.
Iachello and Arima, The Interacting Boson Model.
Course content
The main content of this course includes:
Basic concepts of Lie groups and Lie algebras
Lie groups and Lie transformation groups, infinitesimal generators, basic properties of Lie groups (Lie’s three theorems, connectivity and coverage), Lie algebras
Bases of Lie algebras, Killing metric, structure of Lie algebras (solvable, nilpotent, simple, semisimple, decomposition of Lie algebras), Casimir operators
Semisimple Lie algebras
Canonical form of Lie algebras, Cartan-Weyl basis
Root system of semisimple Lie algebras, Dynkin diagram
Determination of roots
Realization of Lie algebras: Cartan-Weyl basis, Chevalley basis, fermion and boson realizations
Representation of Lie algebras
Weight systems
Irreducible tensors and the Young tableaux
Representation of classical Lie algebras
Casimir operators
Decomposition of representations
Branching rules of Lie algebras
Decomposition of direct products of representations, Clebsch-Gordon coefficients and Wigner-Eckart theorem
Racah theorem and isoscalar factors
Spacetime symmetry and applications
Lorentz group and its representations
Applications of the Lorentz group and the Poincare group
Applications of Lie algebras to hadron structures and strong interactions
Quark structure of light-flavor hadrons and many-quark states
Chiral symmetry and its breaking
Gauge symmetry
Applications of Lie algebras to many-particle systems
Dynamical symmetry of fermionic and bosonic systems
Collective motion of many-particle systems, coherent states
Interacting boson model of nuclear systems, spectrum generating algebra, shape phase transitions
Algebraic models of superconductivity
Essay
We were required to write an essay on any topic about Lie group and Lie algebras. I chose the topic “Branching rules and Gelfand-Tsetlin bases of the classical Lie algebras”.
