Chemistry’s ‘covalent bond’ involves a pair of electrons of opposite spin sharing orbitals of two separate atoms. Atoms are waves on a closed loop. The mass splits into negative and positive parts by a line. We map the upper half-plane, bounded by the line, to the unit disc by ‘wrapping up’ the line into a circle. A massive particle lives in a line bundle, and so it is a loop that goes once around, intersecting the zero section. The velocity of a particle is tangent to its world line in spacetime.
Positrons are ‘holes’ in Dirac’s ‘sea’ of negative-energy electron states. The electron and positron annihilate each other whenever an electron falls into such a hole, with the release of energy. Dirac constructed an equation of motion that avoids negative energy and probabilities. The electron in spacetime oscillates between a massless zig particle and a massless zag particle. There is a continual reversal of velocity, but the direction of spin remains constant. Sections of the bundle decompose into negative and positive parts. Dirac’s operator acts on the sections to describe the particle’s motion.
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Brandenburg Concerto No4-1 BWV1049 - Classical Whimsical by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
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