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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Prof. S. B. Giddings Fall 2010
TA: Erik Perkins
Physics 221A
Relativistic Quantum Field Theory
ASSIGNMENT #1 SOLUTIONS
Problem 1
Starting with some coordinate system in which xµ = (x0, x) we perform a Lorentz trans-
formation on xµ to coordinates in which it takes the form xµ = (x0, |x|, 0, 0), which still
satisfies x0 > 0 because purely spacial rotations act as the identity on the time coordinate.
Then we need only focus on a 2D subspace, in which an orthochronous boost takes the form
µ
=
(
-
-
)
where = v/c, = (1 - 2)-1/2. Applying this boost as xµ = µ
x, we find that
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