sl(2c)so(31)

The situation is analogous to the Relationship Between SO(3) and SU(2), which is discussed extensively on that page.

由 F KLINKER 著作 — In this note we present explicit and elementary formulas for the correspondence between the group of special Lorentz transformation SO+(3, 1), on the one hand, ...

File:Commutative diagram SL(2, C) - SO(3, 1).svg ... Size of this PNG preview of this SVG file: 458 × 450 pixels. Other resolutions: 244 × 240 pixels | 489 × 480 ...

The full finite-dimensional representation theory of the universal covering group (and also the spin group, a double cover) SL(2, C) of SO(3; 1)+ is obtained, ...

1.1 Introduction. The spin homomorphism. SL2(C) → SO1,3(R) is a homomorphism of classical matrix Lie groups. The lefthand group con- sists of 2 × 2 complex ...

2020年3月14日 — By showing that the complexified Lie algebra of the proper Lorentz group SO(3,1) is equivalent to two the direct sum of two complexified SU(2) ...

2021年10月4日 — SL(2,C) double cover of SO+(1, 3) ... I'm trying to understand why SL(2,C) double cover SO+(1, 3). I have read the proof in the book Zee Group ...

2016年12月23日 — In quantum field theory, we use the universal cover of the Lorentz group SL(2,C) instead of SO(3,1). (The reason for this is, of course, ...

2012年10月20日 — You can have X in SL(2,C) act on the Hermitian matrix Y by XYX*, which preserves the determinant. So it preserves the length of the Minkowski ...