Energy-momentum tensor in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Φ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> theory at one loop

The energy-momentum tensor form factors are studied in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi mathvariant="normal">Φ</a:mi><a:mn>4</a:mn></a:msup></a:math> theory to one-loop order with particular focus on the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>D</d:mi></d:math>-term, a particle property which has attracted a lot of attention in the recent literature. It is shown that the free Klein-Gordon theory value of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>D</f:mi></f:math>-term <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi>D</h:mi></h:mrow><h:mrow><h:mi>free</h:mi></h:mrow></h:msub><h:mo>=</h:mo><h:mo>−</h:mo><h:mn>1</h:mn></h:mrow></h:math> is reduced to <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msub><j:mrow><j:mi>D</j:mi></j:mrow><j:mrow><j:mtext>one-loop</j:mtext></j:mrow></j:msub><j:mo>=</j:mo><j:mo>−</j:mo><j:mfrac><j:mrow><j:mn>1</j:mn></j:mrow><j:mrow><j:mn>3</j:mn></j:mrow></j:mfrac></j:mrow></j:math> even if the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi mathvariant="normal">Φ</l:mi><l:mn>4</l:mn></l:msup></l:math> interaction is infinitesimally small. A companion work in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi mathvariant="normal">Φ</o:mi><o:mn>3</o:mn></o:msup></o:math> theory confirms this result which may indicate that it is independent of the type of interaction as long as the scalar theory is renormalizable. Dispersion relations are studied. Various definitions of mean square radii including the mechanical radius are investigated. The findings contribute to a better understanding of the energy momentum tensor properties of particles and their interpretation.