Field Theory Terms

  • internal symmetry - mixes particles among each other, for example, symmetries like SU(N) that mix N quarks among themselves. These internal symmetries rotate fields and particles in an abstract "isotopic space." (1-p34)
  • Gauge symmetry - local internal symmetry (3-p171)
  • Lorentz covariant - an equation is lorentz covariant iff its solutions remain unchanged under a Lorentz transformation (unsure - need reference, see 2-p36)
  • colorless - a state is colorless iff it has no net color or equal amounts of all three colors (unsure - need reference)
  • energy spectrum - (2-p41)
  • adjoint representation - ? (has dimension equal to the number of group generators)
  • defining representation - ?
  • fundamental representation - ?
  • elementary particle - "An elementary particle (EP) is an elementary system whose states in no way can be physically connected to the states of other systems. It's Hilbert space is isolated, i.e. the states of one elementary particle do not form a linear space with those of other systems, that is, the superposition is physically meaningless. The only effect that outside interactions can have on an EP is to change the state within the irreducible representation, i.e., to change its momentum and spin projection. It follows that an EP can have only those internal quantum numbers for which there are absolute superselection rules. This operational definition of an elementary particle reflects the dependence of the concept of elementarity on the nature of interactions, as it should be." (4-p525)
  • symmetry of the Lagrangian - symmetry group of the variational problem (5-p989)
  • Kronecker product - matrix direct product
  • sea gull diagram -
  • tadpole diagram -
  1. Quantum Field Theory by Kaku
  2. Quantum Field Theory of Point Particles and Strings by Hatfield
  3. The Weak Interaction in Nuclear, Particle and Astrophysics by Grotz
  4. Theory of Group Representations and Application by Barut and Raczka
  5. Mathematical Physics by Hassani