scalar field annihilation operator creation operator field
A similar procedure can be applied to the real scalar field ϕ, by promoting it to a quantum field operator 






ϕ
^





{\displaystyle {\hat {\phi }}}

, while the annihilation operator 







a
^





p





{\displaystyle {\hat {a}}_{\mathbf {p} }}

, the creation operator 







a
^





p



†




{\displaystyle {\hat {a}}_{\mathbf {p} }^{\dagger }}

 and the angular frequency 




w


p





{\displaystyle w_{\mathbf {p} }}

are now for a particular p:
