The Lorentz group in the oscillator realization. II. Integral transforms and matrix elements of SO(2,1)

1980 ◽  
Vol 21 (4) ◽  
pp. 636-637 ◽  
Author(s):  
Debabrata Basu ◽  
D. Mitra
Keyword(s):  
Lorentz Group ◽  
Integral Transforms ◽  
Matrix Elements

On non-compact groups. II. Representations of the 2+1 Lorentz group

1965 ◽  
Vol 287 (1411) ◽  
pp. 532-548 ◽  
Keyword(s):  
Hilbert Space ◽  
Direct Product ◽  
Lorentz Group ◽  
Complex Number ◽  
Algebraic Method ◽  
Unitary Representations ◽  
Compact Groups ◽  
Matrix Elements ◽  
Linear Representations ◽  
The Matrix

A simple algebraic method based on multispinors with a complex number of indices is used to obtain the linear (and unitary) representations of non-com pact groups. The method is illustrated in the case of the 2+1 Lorentz group. All linear representations of this group, their various realizations in Hilbert space as well as the matrix elements of finite transformations have been found. The problem of reduction of the direct product is also briefly discussed.

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