## Conservation of Isotopic Spin and Isotopic Gauge Invariance in Physical Review 96 (1), October 1, 1954, pp. 191-196.

Lancaster: American Physical Society, 1954. 1st Edition. RARE FIRST EDITION, FIRST ISSUE IN ORIGINAL WRAPS of the Yang-Mills quantum mechanical theory, introduced in this paper and underappreciated at that time.

The Yang-Mills theory is now the foundation of most of elementary particle theory; it is the mathematical foundation underlying "three of the four fundamental forces of nature that physicists succeeded in unifying in the last half of the 20th century: electromagnetism, the 'weak force' responsible for radioactive decay, and the 'strong force' responsible for holding the nuclei of atoms together" (Gale, World of Mathematics Summary). Yang and Mills proposed a tensor equation that relies on a quantum mechanical property called the 'mass gap.' "The laws of quantum physics stand to the world of elementary particles in the way that Newton's laws of classical mechanics stand to the macroscopic world.

Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. The successful use of Yang-Mills theory (now widely tested and affirmed) to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics" (Clay Mathematics Institute). Item #144

CONDITION & DETAILS: Lancaster: American Physical Society. Volume 96, Number 1, October 1, 1954. Pp. 191-196. (10.5 x 8 inches; 262 x 200mm). Complete issue in original printed wrappers; very, very slight wear at the edges and spine. Near fine condition.

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