General Group Theory Derivation for Selection Rules in Nonlinear Light-Matter Interactions

2019 ◽  
Author(s):  
Gavriel Lerner ◽  
Ofer Neufeld ◽  
Eliayu Bordo ◽  
Liran Hareli ◽  
Georgiy Shoulga ◽  
...  
Keyword(s):  
Group Theory ◽  
General Group ◽  
Selection Rules

General group theory

2002 ◽  
pp. 1-202
Author(s):  
Daniel Gorenstein ◽  
Richard Lyons ◽  
Ronald Solomon
Keyword(s):  
Group Theory ◽  
General Group

The Matrix Equations A = XYZ And B = ZYX and Related Ones

1974 ◽  
Vol 17 (2) ◽  
pp. 179-183 ◽  
Author(s):  
J. L. Brenner ◽  
M. J. S. Lim
Keyword(s):  
Group Theory ◽  
Matrix Theory ◽  
Necessary Condition ◽  
Matrix Equations ◽  
General Group ◽  
Matrix Groups ◽  
The Matrix ◽  
Theory Application ◽  
Theoretical Results

In [15], O. Taussky-Todd posed the problem of title, namely to find X, Y, Z when A, B are given. Clearly if X, Y, Z exist then A, B are either both invertible or both noninvertible.In section 1, the problem is reviewed in case A, B are both invertible. The problem is seen to be fundamentally one of group theory rather than matrix theory. Application of results of Shoda, Thompson, Ree to the general group-theoretical results allows specialization to certain matrix groups.In Section 2, examples and counterexamples are given in case A, B are noninvertible. A general necessary condition for solvability (involving ranks) is obtained. This condition may or may not be sufficient. For dim A=2, 3 the problem is settled: there is always a solution in the noninvertible case.

Particle on a Ring Spectroscopic Selection Rules Determined by Group Theory

2015 ◽  
Vol 92 (12) ◽  
pp. 2165-2169 ◽  
Author(s):  
Victoria S. Jackson ◽  
Darren L. Williams
Keyword(s):  
Group Theory ◽  
Selection Rules
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