Equivalence of gauge-invariant models for massive integer-spin fields

There are several approaches to formulate gauge-invariant models for massive integer-spin fields in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math> dimensions including the following: (i) in terms of symmetric tensor fields <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ϕ</c:mi><c:mrow><c:msub><c:mi>μ</c:mi><c:mn>1</c:mn></c:msub><c:mo>…</c:mo><c:msub><c:mi>μ</c:mi><c:mi>k</c:mi></c:msub></c:mrow></c:msub></c:math>, with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>k</e:mi><e:mo>=</e:mo><e:mi>s</e:mi><e:mo>,</e:mo><e:mi>s</e:mi><e:mo>−</e:mo><e:mn>1</e:mn><e:mo>,</e:mo><e:mo>…</e:mo><e:mo>,</e:mo><e:mn>0</e:mn></e:math>, restricted to be double traceless for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>k</g:mi><g:mo>≥</g:mo><g:mn>4</g:mn></g:math>; and (ii) in terms of a quartet of symmetric tensor fields <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>ψ</i:mi><i:mrow><i:msub><i:mi>μ</i:mi><i:mn>1</i:mn></i:msub><i:mo>…</i:mo><i:msub><i:mi>μ</i:mi><i:mi>k</i:mi></i:msub></i:mrow></i:msub></i:math>, of rank <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>k</k:mi><k:mo>=</k:mo><k:mi>s</k:mi><k:mo>,</k:mo><k:mi>s</k:mi><k:mo>−</k:mo><k:mn>1</k:mn><k:mo>,</k:mo><k:mi>s</k:mi><k:mo>−</k:mo><k:mn>2</k:mn><k:mo>,</k:mo><k:mi>s</k:mi><k:mo>−</k:mo><k:mn>3</k:mn></k:math>. We demonstrate that these formulations in Minkowski space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi mathvariant="double-struck">M</m:mi><m:mi>d</m:mi></m:msup></m:math> are equivalent to the gauge-invariant theory for a massive integer-spin field proposed in 1989 by Pashnev. We also make use of the Klishevich-Zinoviev theory in <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi mathvariant="double-struck">M</p:mi><p:mi>d</p:mi></p:msup></p:math> to derive a unique generalization of the Singh-Hagen model for a massive integer-spin field in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>d</s:mi><s:mo>&gt;</s:mo><s:mn>4</s:mn></s:math> dimensions. Published by the American Physical Society 2024