Posts filled under #ayar

An extract on #ayar

Although professional wrestling is worked, there is a high chance of injury, and even death. Strikes are often stiff especially in Japan and in independent wrestling promotions such as Combat Zone Wrestling and Ring of Honor. The ring is often made out of 2 by 8 timber planks. There have been many brutal accidents, hits and injuries. Many of the injuries that occur in pro wrestling are shoulders, knee, back, neck, and rib injuries. Professional wrestler Davey Richards said in 2015 "We train to take damage, we know we are going to take damage and we accept that." Less than 25 years after the 1990 WrestleMania VI, one third of its 36 competitors had died including Andr the Giant and main event winner The Ultimate Warrior (all of these deaths had occurred before the age of 64).

Pauli vectors elegantly map these commutation and anticommutation relations to corresponding vector products. Adding the commutator to the anticommutator gives [ a , b ] + { a , b } = ( a b b a ) + ( a b + b a ) 2 i a b c c + 2 a b I = 2 a b {\displaystyle {\begin{aligned}\left[\sigma _{a},\sigma _{b}\right]+\{\sigma _{a},\sigma _{b}\}&=(\sigma _{a}\sigma _{b}-\sigma _{b}\sigma _{a})+(\sigma _{a}\sigma _{b}+\sigma _{b}\sigma _{a})\\2i\varepsilon _{abc}\,\sigma _{c}+2\delta _{ab}I&=2\sigma _{a}\sigma _{b}\end{aligned}}} so that, Contracting each side of the equation with components of two 3-vectors ap and bq (which commute with the Pauli matrices, i.e., apq = qap) for each matrix q and vector component ap (and likewise with bq), and relabeling indices a, b, c p, q, r, to prevent notational conflicts, yields a p b q p q = a p b q ( i p q r r + p q I ) a p p b q q = i p q r a p b q r + a p b q p q I . {\displaystyle {\begin{aligned}a_{p}b_{q}\sigma _{p}\sigma _{q}&=a_{p}b_{q}\left(i\varepsilon _{pqr}\,\sigma _{r}+\delta _{pq}I\right)\\a_{p}\sigma _{p}b_{q}\sigma _{q}&=i\varepsilon _{pqr}\,a_{p}b_{q}\sigma _{r}+a_{p}b_{q}\delta _{pq}I~.\end{aligned}}} Finally, translating the index notation for the dot product and cross product results in