Is there an clear way to state truncation? How can I express that if an expression evaluates to a negative number, I assign it a value of zero? Is it possible to do this without repeating the function twice?
Here is an example
$$f(\vec{\phi})=\begin{cases}
 f(\vec{\phi}) & \text{for}\; f(\vec{\phi}) \gt 0 \\\
 0  & \text{for}\; f(\vec{\phi})\lt 0.
\end{cases}$$

It sounds like you are looking for $f^+(x) = \frac{f(x) + |f(x)|}{2}$. Positive values will evaluate to $f(x)$, but negative values will be taken to $0$, but this also repeats the expression so I hope that you were merely looking to avoid a piecewise definition.
