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Unformatted text preview: Lecture 2 7 Sep 26, 2002 2 Tools of Particle Physics One of the most obvious tools is Mathematics. Physics without mathematics is is only play and guess- work. Mathematics is in fact both a tool as well as a guide to new ideas in physics. Many new concepts were born by studying in detail the consequences of a particular theoretical framework. Quite often, detailed predictions following from a theory are compute-intensive, and require new mathematical techniques to be developed. Since the time of Newton and Keppler, the development of mathematics and physics have gone hand-in-hand. Recent theoretical developments in quantum gravity and string theory are exceedingly mathematical in nature and have spurred new developments in the field of to- pology. In this course, we will keep the use of mathematics at an appropriate level, requiring only simple calculus, some notion of differential equations, and some basic matrix algebra. 2.1 Units The usual m, kg, s units present an evident mismatch with the scales used in practical calculations of particle properties and interactions; typical length, masses, and energies are...
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