MOLECULES AS QUANTUM SHAPES AND HOW THEY VIOLATE P AND T

Abstract

A geometric shape is a rigid shape in n-dimensional Euclidean space. These shapes commonly occur in the Born-Oppenheimer approximation in molecular physics, and collective models of nuclei. Abelian and non-Abelian generalizations of the vacuum angle of gauge theories are realized in the quantum theory of shapes. In this paper, such generalizations are presented in the language of modern quantum physics and it is shown that parity, [Formula: see text], and time reversal, [Formula: see text], are violated in certain of these quantum theories. However, the combined symmetry [Formula: see text] of parity composed with time reversal generally remains a good symmetry, just as in gauge theories. The exceptions are the quantum theories of staggered conformations which can violate only [Formula: see text]. The mechanism responsible for the loss of these symmetries is a generalization of the vacuum angle mechanism for the same effect. An important result of the present analysis is the demonstration that geometric shapes, molecules in the Born-Oppenheimer approximation, and nuclei in the collective model description furnish concrete systems which upon quantization discriminate between left- and right-handed coordinates even though this distinction is entirely absent in their classical descriptions.