= Local Lagrangian argument for CPT invariance
Under <CPT>, a Hermitian local tensor monomial picks up a minus sign for each Lorentz vector index, including derivative indices. A <Lorentz scalar> contracts all such indices, so the total sign is positive; charged terms are exchanged with their <Hermitian conjugates>. Therefore a local Hermitian <Lagrangian density> obeys $\Theta\mathcal L(x)\Theta^{-1}=\mathcal L(-x)$, leaving its <action> invariant. This field-level argument illustrates the <CPT theorem> for ordinary scalar, spinor and vector theories; the axiomatic theorem also uses positive energy and <microcausality>.
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