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- W4231089529 abstract "By using a characterization of the concept of analytic representation and a variational approach to self-adjointness introduced in a preceding paper, we prove a theorem, according to which a necessary and sufficient condition for a class C2, regular, tensorial, quasi-linear system of field equations to admit an ordered direct analytic representation in terms of the Lagrange equations in a region R of its variables is that the system is self-adjoint in R. We point out as a first corollary that if the ordering requirement is removed from the definition of analytic representation, then the condition of self-adjointness of the field equations is only sufficient for the existence of a Lagrangian density. We then provide as a second corollary a methodology for the computation of the Lagrangian density for the representation of self-adjoint quasi-linear tensorial field equations. This methodology is also particularized for ordinary semilinear systems of tensorial field equations through a third corollary. The above results are interpreted from the viewpoint of interactions. We first recover, through a fourth corollary, the conventional structure of the total Lagrangian density LTot = Σ1 anLFree(a) + LInt for the semilinear form of the field equations, and then introduce through a fifth corollary a generalized structure of the type LTot = Σ1 anLInt, I(a)LFree(a) + LInt.II for t representations of the field equations in the quasi-linear form. Therefore, our analysis seems to indicate that a general form of representing interacting fields is characterized by (n+1)-interaction terms in the Lagrangian: n multiplicative terms and one additive term to the Lagrangian for the free fields." @default.
- W4231089529 created "2022-05-11" @default.
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- W4231089529 date "1977-02-01" @default.
- W4231089529 modified "2023-09-26" @default.
- W4231089529 title "Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equations" @default.
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- W4231089529 doi "https://doi.org/10.1016/s0003-4916(97)90005-1" @default.
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