The Theory of Groups and Quantum Mechanics

That spacetime is equipped with a (pseudo) Riemannian metric is a fundamental postulate of the General Theory of Relativity. Since the Riemannian type of metric is only one of a rich variety of conceivable metric forms, it is reasonable to ask what the fundamental characteristics of the Riemannian form are that single it out. As discussed in subsections 4.5, 4.6 and 4.7, Weyl analyzed this problem of space, the Raumproblem, in a series of articles (Weyl, 1922a, 1922b, 1923f). Weyl (1949b, p. 400) himself noted that his interest in the philosophical foundations of the General Theory of Relativity motivated his analysis of the representations and invariants of the continuous groups, “I can say that the wish to understand what really is the mathematical substance behind the formal apparatus of relativity theory led me to the study of representations and invariants of groups; and my experience in this regard is probably not unique”.

Group Theory and its Applications

Study of the stretching modes of the arsine molecule

Vibrational modes of the stibine molecule

Algebraic calculation of vibrational energy levels for polyatomic molecules XH3 and XH4: application to ammonia and silane

Unitary Approach to Vibrational Spectra of Tetrahedral Molecules: Generalized Infrared Intensity Model

We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups . We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.

V. Boujut

Papers

Unitary Approach to Vibrational Spectra of Tetrahedral Molecules: Generalized Infrared Intensity Model

Algebraic time-reversal operation

Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models