QB_PH_SEC9_030: Particle Physics & Fundamental Interactions

Which of the following physical quantities is/are classified as an axial vector (pseudovector) that does NOT flip sign under spatial coordinate inversion (parity operation $\vec{r} \to -\vec{r}$)?

Correct Answer

### Step-by-Step Multi-Select Evaluation: 1. **Definition of Parity Inversion ($\mathcal{P}$)**: $\vec{r} \xrightarrow{\mathcal{P}} -\vec{r}, \quad \nabla \xrightarrow{\mathcal{P}} -\nabla, \quad t \xrightarrow{\mathcal{P}} t$ 2. **Evaluation of Candidates**: - **Option A (Orbital Angular Momentum $\vec{L}$)**: $\vec{L} = \vec{r} \times \vec{p} \xrightarrow{\mathcal{P}} (-\vec{r}) \times (-\vec{p}) = +(\vec{r} \times \vec{p}) = +\vec{L}$ Invariance under inversion classifies $\vec{L}$ as an **axial vector**. (CORRECT) - **Option B (Magnetic Induction $\vec{B}$)**: From Biot-Savart law $\vec{B} \propto \int \frac{I d\vec{l} \times \hat{r}}{r^2} \xrightarrow{\mathcal{P}} \frac{(-d\vec{l}) \times (-\hat{r})}{r^2} = +\vec{B}$. Classifies $\vec{B}$ as an **axial vector**. (CORRECT) - **Option C (Electric Dipole $\vec{d}$)**: $\vec{d} = q \vec{r} \xrightarrow{\mathcal{P}} q(-\vec{r}) = -\vec{d}$ Odd parity classifies $\vec{d}$ as a **polar vector**. (INCORRECT) - **Option D (Linear Momentum $\vec{p}$)**: $\vec{p} = m \frac{d\vec{r}}{dt} \xrightarrow{\mathcal{P}} m \frac{d(-\vec{r})}{dt} = -\vec{p}$ Odd parity classifies $\vec{p}$ as a **polar vector**. (INCORRECT) 3. **Conclusion**: Options A and B are correct.