Kinetic term

Template:Short description Template:Unreferenced stub In physics, a kinetic term is the part of the Lagrangian that is bilinear in the fields (and for nonlinear sigma models, they are not even bilinearTemplate:Clarification needed), and usually contains two derivatives with respect to time (or space); in the case of fermions, the kinetic term usually has one derivative only. The equation of motion derived from such a Lagrangian contains differential operators which are generated by the kinetic term. Unitarity requires kinetic terms to be positive.

In mechanics, the kinetic term is

$T=\frac{1}{2}{\dot{x}}^2=\frac{1}{2}{\left(\frac{\partial x}{\partial t}\right)}^2.$

In quantum field theory, the kinetic terms for real scalar fields, electromagnetic field and Dirac field are

$T=\frac{1}{2}{\partial }_{\mu }\mathrm{\Phi }{\partial }^{\mu }\mathrm{\Phi }+\frac{1}{4g^2}{F}_{\mu \nu }{F}^{\mu \nu }+i\overline{\psi }{\gamma }^{\mu }{\partial }_{\mu }\psi .$

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