What does it mean to have a divergent path integral in a QFT?

More specifically, if $$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty $$ What does this mean for the QFT of the field $\phi $?

The field $\phi$ has action $$\int\left(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi+V(\phi)\right)\mbox{d}vol$$

What does it mean to have a divergent path integral in a QFT?

More specifically, if $$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty $$ What does this mean for the QFT of the field $\phi $?

The field $\phi$ has action $$S[\phi]=\int\left(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-V(\phi)\right)\mbox{d}vol$$ where we use Minkowski signature $(+,-,-,-)$.

What does it mean to have a divergent path integral in a QFT?

More specifically, if $$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty $$ What does this mean for the QFT of the field $\phi $?

What does it mean to have a divergent path integral in a QFT?

More specifically, if $$\int e^{i S[\phi]/\hbar} D\phi (t)=\infty $$ What does this mean for the QFT of the field $\phi $?

The field $\phi$ has action $$\int\left(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi+V(\phi)\right)\mbox{d}vol$$