phase transformation theory

Statistical mechanics is one of the main research directions of Yang Zhenning. His characteristic in statistical mechanics is to strictly solve and analyze the general model rooted in physical reality, so as to grasp the essence and essence of the problem. From 65438 to 0952, Yang Zhenning and his collaborators published three important papers on phase transition. The first paper is about the spontaneous magnetization of two-dimensional Ising model, which he independently completed the year before last, and obtained the critical exponent of 1/8. This is the longest calculation that Yang Zhenning has ever done. Ising model is the most basic but extremely important model in statistical mechanics, but its importance in theoretical physics was not widely recognized until 1960s. 1952, Yang Zhenning also cooperated with Li Zhengdao to complete and publish two papers on phase transition theory. Two articles were submitted and published at the same time, which aroused Einstein's interest. In this paper, the analytic properties of giant partition function are studied by analytic continuation method, and it is found that the distribution of its roots determines the state equation and phase transition properties, which eliminates the suspicion that different thermodynamic phases can exist under the same interaction. The climax of these two papers is the unit circle theorem in the second paper, which points out that the zero point of the giant partition function of the lattice gas model attracting interaction lies on the unit circle on the complex plane.

Boson many-body problem

Out of his interest in liquid helium superfluid, Yang Zhenning published or completed a series of papers on thin boson multibody systems with his collaborators around 1957. First, he published two papers with Huang and Luttinger, and applied the pseudopotential method to this field. After writing the article "Is parity conserved in weak interaction", while waiting for the experimental results, the correct ground state energy correction was obtained by double collision method, and then the same results as Huang and Huang were obtained by pseudo potential method. The most surprising energy correction they got was the famous square root correction term, but it could not be verified by experiments at that time. However, with the development of cold atomic physics, this correction term has been confirmed by experiments.

Young-Baxter equation

In 1960s, Yang Zhenning found the strict solution of quantum statistical model by trying to find off-diagonal long program model. 1967, it was found that the fermion quantum many-body problem in the repulsive potential of 1 dimensional δ function could be transformed into a matrix equation, which was later called Yang-Baxter equation (because Baxter also found this equation in another problem of 1972). In 1967, Yang Zhenning also wrote an article published in the following year, further discussing the problem of S matrix. Later, it was found that Yang -—Baxter equation is an extremely important equation in mathematics and physics, which is closely related to kink theory, braid group, Hopf algebra and even string theory. The 1 dimensional fermion problem discussed by Yang Zhenning is very important in the experimental study of cold atoms. The nested Bethe hypothesis method he invented in this paper was used by Lieb and Wu Fayue to solve the 1 dimensional Hubbard model the following year. Hubbard model later became the basis of many theoretical studies on high temperature superconductivity.

Exact solution of boson in repulsive potential of 1 dimensional δ function at finite temperature

In 1969, Yang Zhenning and Yang Zhenping pushed the boson problem in the repulsive potential of 1 dimensional δ function to a finite temperature. This is the first time in history that a quantum statistical model of interaction is obtained at a finite temperature (T >). This model and results were later realized and verified by experiments in the cold atomic system.

Theoretical explanation of superconducting magnetic ionization

196 1 year, through close communication with Fei Zhengqing experimental group, Yang Zhenning and byers theoretically explained the superconducting magnetic ionization discovered by the experimental group, proved that electron pairing can lead to observed phenomena, clarified the basic principle of electromagnetic field without introducing new principles, and corrected the mistakes of London reasoning. In this work, Yang Zhenning and byers applied gauge transformation technique to condensed matter system. Related physics and methods were later widely used in the study of superconductivity, superfluidity and quantum Hall effect.

Off-diagonal long-range order

1962, Yang Zhenning put forward the concept of "long-range order from two angles", thus describing the essence of superfluidity and superconductivity in a unified way, and deeply discussing the root of flux ionization. This is a key concept of contemporary condensed matter physics. From 1989 to 1990, Yang Zhenning found the eigenstate with off-diagonal long program in the Hubbard model closely related to HTS, and found its SO(4) symmetry with Zhang Shousheng.

Parity non-conservation in weak interaction

Symmetry is an important embodiment of the beauty of physics, and it is also one of the themes of theoretical physics in the 20th century. From classical physics and crystal structure to quantum mechanics and particle physics, symmetry analysis is a powerful tool in physics. Yang Zhenning's many contributions to particle physics show that he is good at symmetry analysis. He can often use symmetry accurately, get results quickly with elegant methods, and highlight the essence and ingenuity. 1999, Yang Zhenning was called "the king of symmetry" at an academic conference in Brook, Si Tong.

1950, Yang Zhenning's paper on p0 decay and his paper with Tiomno on phase factor in β decay established his leading position in this field. 1956, the mystery of θ-τ is the most important problem in particle physics. At that time, there was a general discussion about whether parity could not be conserved. Yang Zhenning and Li Zhengdao moved from the specific physical problem θ-τ to a more general problem, put forward the possibility that parity is conserved in strong interaction and electromagnetic interaction, but not necessarily in weak interaction, separated the decay process dominated by weak interaction, and then found that there was no experiment to prove whether parity was conserved in weak interaction before. They also pointed out several key weak interaction experiments to test whether parity is conserved in weak interaction. 1in the summer of 956, Wu Jianxiong decided to do one of several experiments they pointed out about the decay of 60Co β. In June 5438+the following year 10, the experimental group led by her proved that parity is indeed not conserved in weak interaction, which caused great shock in the whole physics field. Because of this work, Yang Zhenning and Li Zhengdao won the 1957 Nobel Prize in Physics.

Three kinds of discrete symmetry: time reversal, charge yoke and parity

Because he questioned whether parity is conserved in weak interaction, Oehme wrote to Yang Zhenning in August 1956, asking about the relationship among three discrete symmetries in weak interaction: parity (P), charge * * * yoke (C) and time reversal (T). This led Yang Zhenning, Li Zhengdao and Hermite to publish a paper 57e to discuss the relationship between the non-conservation of P, C and T respectively. This paper plays a decisive role in the theoretical analysis of CP non-conservation in 1964.

Theoretical discussion on high energy neutrino experiment

1960, in order to get more information about weak interaction experiments, Li Zhengdao and Yang Zhenning discussed the importance of high-energy neutrino experiments in theory by using the ideas of experimental physicist Schwartz. This is the first theoretical analysis of neutrino experiment, which leads to many important research work later.

Phenomenological framework of CP non-conservation

1964 found that CP is not conserved, which led many articles to guess its root cause. Yang Zhenning and Wu Dajun ignored the theoretical speculations that were divorced from reality, but made a phenomenological analysis of the non-conservation phenomenon of CP, and established a phenomenological framework for the later analysis of such phenomena. This reflects Yang Zhenning's down-to-earth style and clearly shows that he is influenced by Fermi.

Young-Mills gauge field theory

1954 Yang-Mills gauge field theory (that is, non-Abelian gauge field theory) was published. This theory, which was not valued by physics at that time, developed into a standard model through the concept of spontaneous symmetry breaking introduced by many scholars in the 1960s and 1970s. This is generally regarded as all the achievements of basic physics in the second half of the 20th century.

Yang Zhenning and Mills' paper, from a mathematical point of view, is a generalization from Abelian gauge field theory to non-Abelian gauge field theory. From the physical point of view, this generalization is used to develop new basic rules of interaction.

Among the four basic interactions that dominate the world, the weak current interaction and the strong interaction are described by Young-Mills theory, and Einstein's general theory of relativity describing gravity is also similar to Young-Mills theory. Yang Zhenning called it "symmetrical dominant force". Young-Mills theory is a great physical achievement in the second half of the 20th century. Young-Mills equation, Maxwell equation and Einstein equation * * * have extremely important historical position.

Integral form of gauge field theory

Yang-Mills theory also pushes the relationship between physics and mathematics to a new height. Around 1970, Yang Zhenning devoted himself to studying the integral form of gauge field theory and discovered the importance of non-integrable phase factor, thus realizing that gauge field has profound geometric significance.

Correspondence between gauge field theory and fiber bundle theory

In 1975, Yang Zhenning and Wu Dajun published a paper 75c, which gave a comprehensive description of electromagnetism and Yang-Mills field theory with the concept of non-integrable phase factor, discussed Aharonov—Bohm effect and magnetic monopole, and revealed the connection between gauge field and fiber bundle in geometry. This paper is accompanied by a dictionary, which accurately translates the basic concepts of gauge field theory in physics into the basic concepts of fiber bundle theory in mathematics. This dictionary aroused people's extensive interest in mathematics and greatly promoted the successful cooperation between mathematics and physics in the next few decades.