In this work we examine ways to extend s-equivalence to field theory. S-equivalent Lagrangians lead to the same classical behavior of systems as conventional Lagrangians, but generally result in different quantum behavior of the systems. We first review ways to construct s-equivalent Lagrangians for discrete systems and later we generalize and apply them to continuous systems. In particular we demonstrate that construction of s-equivalent Lagrangians with non-Noether symmetries is problematic for continuous systems, first non-Noether symmetries may not exist like in the case of the Klein-Gordon equation, or may lead to trivial equivalence like in the case of the Dirac equation. We show that it is nevertheless possible to construct s-equivalence for continuous systems by going t...[ Read more ]

In this work we examine ways to extend s-equivalence to field theory. S-equivalent Lagrangians lead to the same classical behavior of systems as conventional Lagrangians, but generally result in different quantum behavior of the systems. We first review ways to construct s-equivalent Lagrangians for discrete systems and later we generalize and apply them to continuous systems. In particular we demonstrate that construction of s-equivalent Lagrangians with non-Noether symmetries is problematic for continuous systems, first non-Noether symmetries may not exist like in the case of the Klein-Gordon equation, or may lead to trivial equivalence like in the case of the Dirac equation. We show that it is nevertheless possible to construct s-equivalence for continuous systems by going to momentum space and constructing s-equivalent Klein-Gordon Lagrangian. Although this Lagrangian describes free particles it has apparent interaction, however first order tree level calculations show that it behaves like a free Lagrangian. Finally we use field redefinition to construct yet another s-equivalent Klein-Gordon Lagrangian, and demonstrate that it would be stable after quantization. We note that using auxiliary conditions to generate s-equivalence may also affect the classical behavior of systems.