Round 3: Tossup 7

These operators exhibit eightfold periodicity in dimension in a manner analogous to the Bott periodicity theorem. These operators are moved within a quadrilinear product using Fierz rearrangement identities. The product of these operators is multiplied by a Levi-Civita (“LEV-ee CHEE-vee-ta”) symbol in the Rarita–Schwinger equation. (10[1])Pairwise commutations of these operators form a representation of the Lorentz algebra. These operators generate the real Clifford algebra with signature (-5[1])1,3. (-5[2])The contraction of these operators with an arbitrary covariant vector is often written using Feynman (-5[1])slash notation, such as in (10[1])a 1928 equation where they are composed (-5[1])with the (-5[1])four-gradient. These four-dimensional operators are (-5[1])obtained by taking (-5[1])outer products of Pauli matrices. (-5[2])For 10 points, name these operators that act on spinors (“spinners”) in the Dirac equation. (10[2])■END■ (10[3]0[13])

Back to tossups

Buzzes

Summary