Canonical Quantization of Scalar Fields — Mark Srednicki
Physics — QFT · chiral-symmetry-breaking
Problem
Suppose that the color group is SO(3) rather than SU(3), and that each quark flavor is represented by a Dirac field in the 3 representation of SO(3).
a) With nF flavors of massless quarks, what is the nonanomalous flavor symmetry group?
b) Assume the formation of a color-singlet, Lorentz scalar, fermion condensate. Assume that it preserves the largest possible unbroken subgroup of the flavor symmetry. What is this unbroken subgroup?
c) For the case nF=2, how many massless Goldstone bosons are there?
d) Now suppose that the color group is SU(2) rather than SU(3), and that each quark flavor is represented by a Dirac field in the 2 representation of SU(2). Repeat parts (a), (b), and (c) for this case. Hint: at least one of the answers is different!