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spaghetti3451
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Homework Statement
Is the transformation ##Y:(t,x,y,z)\rightarrow (t,x,-y,z)## a Lorentz transformation? If so, why is it not considered with P and T as a discrete Lorentz transformation? If not, why not?
Homework Equations
The Attempt at a Solution
A Lorentz transformation ##\Lambda## satisfies the relation ##\Lambda^{T}g\Lambda = \Lambda##, where ##g## is the Minkowski metric.
In our case, the transformation ##Y = \text{diag}(1,1,-1,1)##.
Therefore, ##Y^{T}gY = \text{diag}(1,1,-1,1) \cdot{\text{diag}(1,-1,-1,-1)}\cdot{\text{diag}(1,1,-1,1)} = \text{diag}(1,-1,-1,-1) =## the parity operator.
Therefore, the relation ##Y^{T}gY = Y## is not satisfied.
Therefore, ##Y## is not a Lorentz transformation.
Is my answer correct?