The charge operator, $\hat{Q},$ is an [observable](Observable.md) whose [eigenvalue](Observable.md#Physical%20meaning%20of%20_Observables_) is a positive number for [particles](Quantum%20mechanical%20particles.md) and whose eigenvalue is a negative number for [antiparticles.](Antiparticles) # Algebraic properties of the charge operator In terms of the charge operator, $\hat{Q},$ where $i$ is a basis element of [$\mathfrak{u}(1),$](U(1).md#Corresponding%20Lie%20Algebra%20to%20mbox%20U%201) the unitary representation is given by $U'(L)= e^{-i\hat{Q}}=-i\hat{Q}$ and $U(\theta)= e^{-i\theta\hat{Q}}$ %%pg. 479 of Woit%% %%thread on stack exchange https://physics.stackexchange.com/questions/282863/charge-operator-action-in-qft%% #QuantumMechanics/QuantumMeasurement/QuantumObservables #QuantumMechanics/RelativisticQuantumMechanics #QuantumMechanics/QuantumFieldTheory