Two-dimensional theory of chirality. II. Relative chirality and the chirality of complex fields

摘要

Chirality can equally be correctly viewed as a dichotomous symmetry property, as in Kelvin's historical conception, and as a continuous phenomenon. This highly paradoxical result is proved, in this and the previous article (I) [Le Guennec, J. Math. Phys. 41, 5954 (2000)], in the case of the basic ingredient of quantum mechanics, square-integrable (L-2) wave functions. In the continuous conception, chirality appears as the combination of two complementary forms-absolute and relative chirality. Accordingly, while (I) focused on the conceptual issue and on the 2D theory of absolute chirality, this article focuses on 2D relative chirality. We show that relative chirality is a continuous phenomenon described by relative radial functions and relative chiral loops whose features are surprisingly close to those of their absolute counterparts. This is illustrated on a 2D model of cis-trans isomerism. We then show that chirality as such is the "addition" of absolute and relative chirality just as a vector is the addition of its projection on a basis. As a test of versatility, the continuous conception of chirality is extended to 2D complex fields and Fourier transforms. Why this conception of chirality is possible in L-2 spaces is tentatively discussed. (C) 2000 American Institute of Physics. [S0022-2488(00)02207-6]. [References: 9]