SEVERAL PHYSICAL CONCEPTS UNDER A UNIFIED PERSPECTIVE: INSIGHTS FROM THE SU(1,1) GROUP

Revisiting seemingly unrelated physical concepts from a unified perspective is not only a scientific research method but also aids in physics education, facilitating students' comprehensive understanding. Using a comparative analysis research method, this paper takes the SU(1,1) group as an example to discuss how to view several concepts in different fields of physics from a unified perspective, covering Lorentz transformations in special relativity, simple harmonic oscillators in quantum mechanics, Bogoliubov transformations in condensed matter physics, and squeezed states in quantum optics. By re-examining the examples involved in this paper from the perspective of the SU(1,1) group, on one hand, it deepens the understanding of the relevant concepts, and on the other hand, it helps to deepen students' understanding of the concept of symmetry. Revisiting several seemingly unrelated concepts in the field of physics from a unified perspective not only providesa new perspective for scientific research but also greatly promotes the depth and breadth of physics education. This paper takes the SU(1,1) group as an example to explore how to apply this mathematical tool to different fields of physics, thereby revealing its core role in different physical phenomena. The paper first analyzes the Lorentz transformation in special relativity, demonstrating how the SU(1,1) group helps us to understand the physical essence of this transformation more deeply. Then, the paper turns to quantum mechanics to discuss the application of the SU(1,1) group in describing the problem of the simple harmonic oscillator, revealing its key role in the evolution of quantum states. In the field of condensed matter physics, the paper discusses the unified description of Bogoliubov transformations, emphasizing the importance of the SU(1,1) group in understanding phase transitions in condensed matter systems. The paper also explores squeezed states in quantum optics, showing the application of the SU(1,1) group in describing the characteristics of light field squeezed states, further revealing its potential in quantum information processing. Through the perspective of the SU(1,1) group, this article summarizes the common mathematical foundations and universal physical laws of these physical concepts, and it not only deepens the understanding of these physical concepts but also promotes students' in-depth understanding of the concept of symmetry, thus providing a new perspective and method for physics education and research.