Exercise List #1

Classical Field Theory

October 14, 2009

1. Check if the one-dimensional Newton equation

¨

x = F (x, ˙

x, t)

is invariant under the following transformations:

• x

0

= x + vt +

1
2

bt

2

, t

0

= t,

• x

0

= f (x), t

0

= t,

• x

0

= x, t

0

= g(t).

2. Describe (both qualitatively and quantitatively) the following special relativistic

phenomena:

• time dilation,

• length contraction,

• Doppler effect.

3. Derive the form of a Lorentz matrix for a boost along one of the coordinate system’s

axes, with the rapidity parameter.