C-R-T Fractionalization in the First Quantized Hamiltonian Theory

Summary

The paper discusses the concept of C-R-T (charge, reflection, and time-reversal) fractionalization in the first quantized Hamiltonian theory. It defines the Majorana fermion as a real Grassmannian field acting as an irreducible representation of the 8-fold real Clifford algebra. The authors analyze the internal symmetry of the Clifford algebra and find an 8-fold periodicity in the symmetry group. They also discuss the mass extension and domain wall reduction, and show that the CRT-internal symmetries can act non-trivially on the mass manifold.

Highlights

• The paper introduces the concept of C-R-T fractionalization in the first quantized Hamiltonian theory.
• The Majorana fermion is defined as a real Grassmannian field acting as an irreducible representation of the 8-fold real Clifford algebra.
• The authors analyze the internal symmetry of the Clifford algebra and find an 8-fold periodicity in the symmetry group.
• The mass extension and domain wall reduction are discussed.
• The CRT-internal symmetries can act non-trivially on the mass manifold.
• The paper also discusses the symmetry reduction under domain wall reduction.
• The results are summarized in various tables and appendices.

Key Insights

• The C-R-T fractionalization is a fundamental concept in understanding the symmetry properties of fermions in different dimensions. The authors' analysis of the internal symmetry of the Clifford algebra reveals an 8-fold periodicity in the symmetry group, which is a crucial insight for understanding the behavior of fermions in various dimensions.
• The definition of the Majorana fermion as a real Grassmannian field acting as an irreducible representation of the 8-fold real Clifford algebra provides a new perspective on the nature of fermions. This definition allows for a more nuanced understanding of the properties of Majorana fermions and their role in various physical systems.
• The discussion of mass extension and domain wall reduction highlights the importance of these concepts in understanding the behavior of fermions in different dimensions. The authors' analysis shows that the CRT-internal symmetries can act non-trivially on the mass manifold, which has significant implications for our understanding of fermionic systems.
• The symmetry reduction under domain wall reduction is a critical aspect of the paper. The authors' analysis shows that the symmetry group of the theory is reduced under domain wall reduction, which has important implications for our understanding of the behavior of fermions in different dimensions.
• The use of tables and appendices to summarize the results is a useful tool for readers. The tables provide a concise summary of the symmetry groups and their properties, while the appendices offer a more detailed analysis of the mathematical structures underlying the theory.
• The paper's focus on the first quantized Hamiltonian theory provides a new perspective on the behavior of fermions. This approach allows for a more detailed analysis of the symmetry properties of fermions and their role in various physical systems.
• The authors' analysis of the CRT-internal symmetries and their action on the mass manifold is a significant contribution to our understanding of fermionic systems. This insight has important implications for our understanding of the behavior of fermions in different dimensions and their role in various physical systems.

Mindmap

Citation

Li, Y.-Y., Wan, Z., Wang, J., Yau, S.-T., & You, Y.-Z. (2024). C-R-T Fractionalization in the First Quantized Hamiltonian Theory (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.11958