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The use of cavity quantum electrodynamical effects, i.e., of vacuumelectromagnetic fields, to modify material properties in cavities has rapidlygained popularity and interest in the last few years. However, there is still ascarcity of general results that provide guidelines for intuitive understandingand limitations of what kind of effects can be achieved. We provide such aresult for the effective interactions between low-energy matter excitationsinduced either directly by their mutual coupling to the cavity electromagnetic(EM) field or indirectly through coupling to mediator modes that couple to theEM field. We demonstrate that the induced interactions are purely electrostaticin nature and are thus fully described by the EM Green's function evaluated atzero frequency. Our findings imply that reduced models with one or a few cavitymodes can easily give misleading results.

Electrostatic nature of cavity-mediated interactions between low-energy matter excitations