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- W4387319782 abstract "We have studied several important aspects of the quantum theory of fields and found that the theory is based in essence upon the theory of relativity. In Chaps. 1 and 21 , we briefly surveyed its essence. In this chapter, we explore the basic formalism and fundamental skeleton of the theory more systematically in depth and in breadth. First, we examine the constitution of the Lorentz group from the point of view of Lie algebra. The Lorentz group comprises two components, one of which is virtually the same as the rotation group that we have examined in Part IV. Another component, on the other hand, is called Lorentz boost, which is considerably different from the former one. In particular, whereas the matrices associated with the spatial rotation are unitary, the matrices that represent the Lorentz boost are not unitary. In this chapter, we connect these aspects of the Lorentz group to the matrix representation of the Dirac equation to clarify the constitution of the Dirac equation. Another point of great importance rests on the properties of Dirac operators $$ mathfrak{G} $$ and $$ overset{sim }{mathfrak{G}} $$ that describe the Dirac equation (Sect. 21.3 ). We examine their properties from the point of view of matrix algebra. In particular, we study how $$ mathfrak{G} $$ and $$ overset{sim }{mathfrak{G}} $$ can be diagonalized through the similarity transformation. Remaining parts of this chapter deal with advanced topics of the Lorentz group from the point of view of continuous groups and their Lie algebras." @default.
- W4387319782 created "2023-10-04" @default.
- W4387319782 creator A5059168563 @default.
- W4387319782 date "2023-01-01" @default.
- W4387319782 modified "2023-10-05" @default.
- W4387319782 title "Basic Formalism" @default.
- W4387319782 cites W4244067739 @default.
- W4387319782 doi "https://doi.org/10.1007/978-981-99-2512-4_24" @default.
- W4387319782 hasPublicationYear "2023" @default.
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