sl(2c)so(31)

1.1Introduction.Thespinhomomorphism.SL2(C)→SO1,3(R)isahomomorphismofclassicalmatrixLiegroups.Thelefthandgroupcon-sistsof2×2complex ...,由FKLINKER著作—InthisnotewepresentexplicitandelementaryformulasforthecorrespondencebetweenthegroupofspecialLorentztransformationSO+(3,1),ontheonehand, ...,File:CommutativediagramSL(2,C)-SO(3,1).svg...SizeofthisPNGpreviewofthisSVGfile:458×450pixels.Otherresoluti...

參考資訊如下
1 The spin homomorphism SL2(C) → SO1,3(R)

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 ...

an explicit description of sl(2, c) in terms of so+(3, 1) and ...

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)

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 ...

Homomorphism from SL(2,ℂ) to Lorentz group 1

How can I see that SL(2,C) is a double cover of SO(3,1)?

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 ...

How is the invariant speed of light enocded in SL(2,C)?

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, ...

Relationship Between SO(3,1) and SL(2,C)

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

Representation theory of the Lorentz group (for ...

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, ...

SL$(2, mathbbC})$ double cover of SO$}^+}$(1, 3)

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 ...

Why SL(2,C) if everything can be derived with SO(3,1) and ...

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) ...