1.1 Particles and Field
Two kinds of dynamics systems:
Motion of a particle or rigid body (with a finite # of DoF
Physical systems (with nondenumerably infinite of DoF -> Fields
Classical Fields:
E(x, t); B(x, t)
(phi(x, t), vec(A)(x, t))
D+1 fields
D -> spatial dimensions
one dimensional string: 1+1 dimensional field theory
Maxwell's eq: 3+1 dimensional field theory
motion of a particle: 0+1 dimensional field theory
1.2 Metric and Other Notations
Bjorken-Drell convention (for relativistic theories
Contravariant coordinates are assumed to be
x^(mu) = (t, x)
mu = 0, 1, 2, 3
x_\mu = \eta_{\mu \nu}x^{\nu} = (t, -x)