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Free field
In physics a free field is a field without interactions, which is described by the terms of motion and mass.
== Description ==
In classical physics, a free field is a field whose equations of motion are given by linear partial differential equations. Such linear PDE's have a unique solution for a given initial condition.
In quantum field theory, an operator valued distribution is a free field if it satisfies some linear partial differential equations such that the corresponding case of the same linear PDEs for a classical field (i.e. not an operator) would be the Euler–Lagrange equation for some quadratic Lagrangian. We can differentiate distributions by defining their derivatives via differentiated test functions. See Schwartz distribution for more details. Since we are dealing not with ordinary distributions but operator valued distributions, it is understood these PDEs aren't constraints on states but instead a description of the relations among the smeared fields. Beside the PDEs, the operators also satisfy another relation, the commutation/anticommutation relations.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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