Nonlocal Lagrangian

In field theory, a nonlocal Lagrangian is a Lagrangian, a type of functional $\mathcal$phi(x) containing terms that are ''nonlocal'' in the fields $\phi(x)$, i.e. not polynomials or functions of the fields or their derivatives evaluated at a single point in the space of dynamical parameters (e.g. space-time). Examples of such nonlocal Lagrangians might be:
* $\mathcal = \frac\big(\partial_x \phi(x)\big)^2 - \fracm^2 \phi(x)^2 + \phi(x) \int \frac \,d^ny.$
* $\mathcal = -\frac\mathcal_\left(1 + \frac\right)\mathcal^.$
* S = \int dt \,d^dx \left psi^*\left(i\hbar \frac + \mu\right)\psi - \frac\nabla \psi^*\cdot \nabla \psi\right- \frac\int dt \,d^dx \,d^dy \, V(\mathbf - \mathbf) \psi^*(\mathbf) \psi(\mathbf) \psi^*(\mathbf) \psi(\mathbf).
* The Wess–Zumino–Witten action.

Actions obtained from nonlocal Lagrangians are called ''nonlocal actions''. The actions appearing in the fundamental theories of physics, such as the Standard Model, are local actions; nonlocal actions play a part in theories that attempt to go beyond the Standard Model and also in some effective field theories. Nonlocalization of a local action is also an essential aspect of some regularization procedures. Noncommutative quantum field theory also gives rise to nonlocal actions.

Quantum measurement
Quantum field theory
Theoretical physics

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