NYCITP, RAINY, ν York
(visiting U. Esta Dual Teoria do Campo)
String theory isn't easy, fool. The title was just a trick to get you to read this abstract. However, we will give a list of simple rote rules that will allow you to do research on strings.
An important idea that is used frequently in high-energy physics is the concept of "Wick rotation", i.e., turning time into space. A geometric way of picturing this is the following: ⇒
This replaces an unfamiliar object with a more familiar one. |
This transformation is explained mathematically in a very simple way through the use of complex numbers: Expressing time in terms of clocks, we treat the 4th dimension x⁴ of time as an imaginary one: | This expresses the mathematical equation x⁴ = ict, which not only makes time imaginary, but also gives it units of space, as the speed of light c = length/time. | In string theory we do a bit more, by mapping linear time, which looks like a circle on a clock, to the complex plane, where it really does become a (unit) circle: | You may recognize these numbers from your study of trigonometry, or @ least you would have if you hadn't learned the subject on a calculator. |
Application of self-homeomorphisms is another method to change geometries in a way that makes them more appealing: ⇒ |
lim |
→nifty |
∑ | where |
the rainbow |
where "dμ" is the pleasure of integration, & we have applied the St(e)r(l)ing approximation.
⎛1 0⎞ |
⎝0 0⎠ |