Complex Inhomogeneous Lorentz Group and Complex Angular Momentum

1966 ◽  
Vol 16 (5) ◽  
pp. 210-211 ◽  
Author(s):  
Eric H. Roffman
Keyword(s):  
Angular Momentum ◽  
Lorentz Group ◽  
Complex Angular Momentum ◽  
Inhomogeneous Lorentz Group

Realizations of generators of complex angular momentum

1990 ◽  
Vol 68 (7-8) ◽  
pp. 599-603
Author(s):  
Shuchi Bora ◽  
H. C. Chandola ◽  
B. S. Rajput
Keyword(s):  
Angular Momentum ◽  
Lorentz Group ◽  
Continuous Spin ◽  
Zero Mass ◽  
Complex Angular Momentum ◽  
General Manner ◽  
Homogeneous Lorentz Group ◽  
Real Mass ◽  
Spin Representations ◽  
Spin Contribution

We use the generators of complex angular momentum in complex c3 space and derive the realizations of the homogeneous Lorentz group for nonzero real mass, zero mass, and imaginary mass systems. We use the appropriate little group for different systems to calculate the modifications in the spin contribution to angular momentum and the unphysical continuous spin representations are shown to be eliminated. We diagonalize the helicity operator in c3 space and obtain the generators of complex angular-momentum operators, which are shown to lead, in a general manner, to the standard helicity representations of the Poincare group for timelike and spacelike systems.

Edth-a differential operator on the sphere

1982 ◽  
Vol 92 (2) ◽  
pp. 317-330 ◽  
Author(s):  
Michael Eastwood ◽  
Paul Tod
Keyword(s):  
Angular Momentum ◽  
Differential Operator ◽  
Lorentz Group ◽  
Space Time ◽  
Conformal Group ◽  
Theory Of Relativity ◽  
Asymptotically Flat ◽  
Group 4 ◽  
Lowering Operator ◽  
Inhomogeneous Lorentz Group

Introduction. In (9) Newman and Penrose introduced a differential operator which they denoted ð, the phonetic symboledth. This operator acts onspin weighted, orspinandconformally weightedfunctions on the two-sphere. It turns out to be very useful in the theory of relativity via the isomorphism of the conformal group of the sphere and the proper inhomogeneous Lorentz group (11, 4). In particular, it can be viewed (2) as anangular momentum lowering operatorfor a suitable representation of SO(3) and can be used to investigate the representations of the Lorentz group (4). More recently, edth has appeared in thegood cut equationdescribing Newman'sℋ-spacefor anasymptotically flatspace-time (10). This development is closely related to Penrose's theory oftwistorsand, in particular, toasymptotic twistors(14).

Sign in / Sign up

Export Citation Format

Share Document