# A Bosonic Field operator in this exponential

#### QFT1995

If i had a bosonic field $\phi(x)$ and I took the exponential in the following way to get the operator $$W=e^{\imath f \phi(x)}$$ where $f$ is a parameter what effect would this have when acting on the vacuum $|0\rangle$? Is it analogous to the space translation operator? Will it transform the vacuum into some state?

Related Quantum Physics News on Phys.org

#### A. Neumaier

Taking the exponential of a distribution is ill-defined and needs a regularization to give it a meaning. The result is a state not described by the original Fock basis.

#### Demystifier

If i had a bosonic field $\phi(x)$ and I took the exponential in the following way to get the operator $$W=e^{\imath f \phi(x)}$$ where $f$ is a parameter what effect would this have when acting on the vacuum $|0\rangle$? Is it analogous to the space translation operator? Will it transform the vacuum into some state?