Classical features, Anderson-Higgs mechanism, and unitarity in Lee-Wick pseudo-electrodynamics

In this paper, the dimensional reduction is applied to the Lee-Wick electrodynamics in which the classical sources are confined on a spatial plane. As result, the Lee-Wick pseudoelectrodynamics is achieved as a nonlocal electromagnetism defined in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>2</a:mn></a:math> dimensions. The Abelian Anderson-Higgs mechanism is so introduced in the Lee-Wick pseudo-electrodynamics through a complex scalar sector in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>1</c:mn><c:mo>+</c:mo><c:mn>2</c:mn></c:math> dimensions, breaking spontaneously the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:math>-gauge symmetry of the nonlocal theory. As consequence, the pseudo-Lee-Wick field acquires a light mass, beyond the usual heavy Lee-Wick mass, that is a natural mass parameter of the theory. After the spontaneous symmetry breaking takes place, classical features of the theory are discussed, as the pseudo-Proca-Lee-Wick electrodynamics, with the field equations and conservation laws. The introduction of Lee-Wick fermions also is proposed, in which it opens the discussion of a viable pseudo-Proca-Lee-Wick quantum electrodynamics in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>1</i:mn><i:mo>+</i:mo><i:mn>2</i:mn></i:math> dimensions. The unitarity at the tree level of the Lee-Wick pseudo-electrodynamics is discussed through the optical theorem.