Ashok Das' Field Theory Ch1 Note

1.1 Particles and Field

Two kinds of dynamics systems:

1. Motion of a particle or rigid body (with a finite # of DoF

2. 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)