Fourier transform with factor $(-1)$ rather than $\frac{1}{\sqrt{2\pi}}$

Question

My physics professor defined the following expression for the Fourier transforms of the current density in space and time: $$ \Delta j_{i}(\mathbf{k}, \omega) \equiv \frac{1}{(2 \pi)^{2}} \iiiint e^{-i(\mathbf{k} \cdot \mathbf{r}-\omega t)} \Delta j_{i}(\mathbf{r}, t) d^{3} r d t $$ where it can be seen that each integral is scaled by a factor of $\frac{1}{\sqrt{2\pi}}$. In the same calculations, he defined the following Fourier transform of the conductivity function: $$ \widetilde{\sigma_{i j}}(\mathbf{k}, \omega) \equiv \iiiint \sigma_{i j}\left(\mathbf{r}^{\prime \prime}, t^{\prime \prime}\right) e^{-i\left(\mathbf{k} \cdot \mathbf{r}^{\prime \prime}-\omega t^{\prime \prime}\right)}(-1)^{4} d^{3} r^{\prime \prime} d t^{\prime \prime} $$ where it appears that each integral is scaled by $(-1)$. Can someone explain why the Fourier transforms might be defined differently?