THESIS
2016
Abstract
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...[
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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.
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