Consider the transformation of the 4-vector (1,0) under a boost in the direction: (1,0)→ (7₁-√²-1), where r= √v²-1 parameterises

Question

Consider the transformation of the 4-vector (1,0) under a boost in the direction:
(1,0)→ (7₁-√²-1),
where r= √v²-1 parameterises the boost.
Writing r = cosh∅  show that the boost corresponds to the transformation matrix Q = exp (σ₃/2)(note that there is no i in our matrix representation).

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