C. N. Yang咋摘了Hermann Weyl的桃子？Yang- Mills 理论和Hermann Weyl的gauge theory是一样的？Yang Mills 发表时Weyl还活着Albert小石头也还活着，Weyl为啥不说是自己的优先权？C. N. Yang此后也反复比较Weyl和Yang- Mills的差异，Weyl种的桃树在哪里，结的果子在哪里？
你是学物理的吗？真是学物理的，规范场理论跳过去了？你不能酸葡萄，C. N. Yang娶了翁，也没带动人都撇下相当的去娶小丫头，恨得被杨抢了女朋友似的。
C. N. Yang咋摘了Hermann Weyl的桃子？Yang- Mills 理论和Hermann Weyl的gauge theory是一样的？Yang Mills 发表时Weyl还活着Albert小石头也还活着，Weyl为啥不说是自己的优先权？C. N. Yang此后也反复比较Weyl和Yang- Mills的差异，Weyl种的桃树在哪里，结的果子在哪里？
你是学物理的吗？真是学物理的，规范场理论跳过去了？你不能酸葡萄，C. N. Yang娶了翁，也没带动人都撇下相当的去娶小丫头，恨得被杨抢了女朋友似的。
C. N. Yang has often highlighted the profound impact of Hermann Weyl’s contributions to physics, particularly emphasizing the significance of Weyl’s work on gauge theory and its influence on modern theoretical physics. Yang’s reflections on Weyl’s work can be summarized by focusing on several key themes:
1. Gauge Symmetry and the Birth of Modern Gauge Theory
Weyl’s Gauge Theory (1918): Hermann Weyl's pioneering work on gauge symmetry was one of the earliest attempts to formulate a unified theory of gravity and electromagnetism. In his theory, Weyl introduced the concept of gauge invariance, proposing that physical laws should remain unchanged under local scale transformations (initially in terms of local changes in length). Although this original idea of gauging scale invariance didn’t hold up to experimental evidence, it laid the groundwork for the gauge principle, which would become a cornerstone of modern physics.
Yang’s Perspective: C. N. Yang has often pointed out that Weyl’s introduction of the gauge principle was an extraordinarily bold and visionary idea. Yang has described Weyl as the "first to see" the potential of local symmetries (gauge symmetries) in physics. Although Weyl’s original theory didn’t survive in its proposed form, the conceptual framework he established proved critical for the development of gauge theories, which later became essential for understanding the fundamental forces of nature.
2. From Weyl’s U(1) Gauge Theory to Yang-Mills Theory
Weyl’s Abelian Gauge Theory: Weyl’s gauge theory was an attempt to describe electromagnetism using a local U(1) gauge symmetry. This idea was one of the earliest formulations of what is now known as electromagnetic gauge theory, which describes the interaction of charged particles with the electromagnetic field.
Yang-Mills Theory (1954): Yang, along with Robert Mills, extended Weyl’s idea of gauge invariance to non-Abelian gauge groups (e.g., SU(2), SU(3)). This generalization led to the creation of Yang-Mills theory, which introduced the concept of gauge fields that correspond to the generators of non-Abelian groups and provided a framework for describing the weak and strong nuclear forces.
Yang’s Acknowledgment of Weyl: C. N. Yang has consistently credited Weyl for his foundational work on gauge invariance. In Yang's view, Weyl’s idea of introducing gauge fields to maintain local symmetry was a profound leap that made the development of Yang-Mills theory possible. Without Weyl’s early work on U(1) gauge symmetry, the formulation of non-Abelian gauge theories might have taken longer to emerge.
3. Weyl’s Role in Symmetry and Geometry in Physics
Symmetry as a Guiding Principle: Weyl was one of the first to deeply appreciate the role of symmetry in physics, not just as a mathematical tool but as a fundamental principle governing physical laws. His work on gauge theory, as well as his contributions to the understanding of group theory in quantum mechanics, emphasized that the structure of physical laws could be understood through symmetry transformations.
Yang’s View on Symmetry: Yang has frequently highlighted Weyl’s profound understanding of symmetry as a guiding principle in theoretical physics. Yang himself was deeply influenced by this, particularly in his work on non-Abelian gauge symmetry, which expanded Weyl’s early ideas into the framework that now underpins the Standard Model of particle physics. Yang regarded Weyl as a visionary who understood that symmetry could dictate the fundamental interactions of nature.
4. Weyl’s Mathematical Elegance and Influence on Quantum Mechanics
Group Theory in Quantum Mechanics: Weyl made significant contributions to the mathematical structure of quantum mechanics, particularly through his work on group theory. His analysis of symmetry groups in quantum mechanics laid the groundwork for understanding how particles and fields transform under various symmetry operations.
Yang on Weyl’s Mathematical Insight: Yang has repeatedly praised Weyl’s mathematical elegance and clarity. In particular, Weyl’s work on the representation theory of Lie groups and Lie algebras provided essential tools for later developments in quantum field theory. For Yang, Weyl’s ability to connect deep mathematical structures with physical principles was a hallmark of his work and had a lasting influence on both quantum mechanics and field theory.
5. Weyl’s Influence on General Relativity and Modern Theoretical Physics
Weyl’s Contributions to General Relativity: In addition to his work on gauge theory, Weyl made significant contributions to the geometric formulation of general relativity, especially through his exploration of spacetime curvature and the development of Weyl curvature. His ideas on the relationship between geometry and physics laid the foundation for later attempts to unify fundamental forces within a geometrical framework.
Yang on Weyl’s Legacy in Unification Theories: Yang has acknowledged Weyl’s foresight in attempting to unify gravity and electromagnetism, even if the exact path Weyl took did not lead to a successful theory. Weyl’s vision of a unified field theory and his belief in the power of symmetry have continued to inspire physicists working on grand unification theories, quantum gravity, and string theory.
6. Yang’s Overall Assessment of Weyl’s Contributions
Influence on Future Generations: C. N. Yang has consistently regarded Weyl as one of the greatest theoretical physicists and mathematicians of the 20th century. He has described Weyl’s work as foundational, especially in the realm of gauge theory and symmetry. Yang often reflects on how Weyl’s ideas provided the intellectual foundation for many of the advances in modern theoretical physics, including the work on gauge fields and non-Abelian symmetries that culminated in the Standard Model.
A Visionary Thinker: Yang saw Weyl as a thinker who was far ahead of his time, with an ability to blend deep mathematical insight with physical intuition. In Yang’s view, Weyl’s contributions to the understanding of gauge invariance and symmetry are of enduring importance, and his ideas continue to shape the direction of theoretical physics to this day.
Conclusion:
C. N. Yang holds Hermann Weyl in the highest regard, recognizing him as a visionary whose contributions to gauge theory, symmetry, and mathematical physics were essential to the development of modern theoretical physics. Yang particularly appreciates Weyl’s bold introduction of gauge invariance and his deep understanding of symmetry principles, which laid the groundwork for the creation of Yang-Mills theory and the gauge theories that now describe the fundamental interactions of nature. Weyl’s influence on Yang and on the broader field of physics is immense, and his work remains a guiding light for those exploring the deep connections between mathematics and the physical world.
