T
he possible description of t
he vacuum of quantum gravity t
hroug
h t
he so called
![](/ft/mat/22_00017701/xx<font color=)
large954.gif" alt="kappa" align="BASELINE" BORDER="0">-Poincaré group is analyzed considering some of t
he consequences of t
his symmetry in t
he pat
h integral formu
lation of non-re
lativistic quantum t
heory. T
his study is carried out wit
h two cases, firstly, a free particle, and finally, t
he situation of a particle immersed in a
homogeneous gravitational field. It will be s
hown t
hat t
he
![](/ft/mat/22_00017701/xx<font color=)
large954.gif" alt="kappa" align="BASELINE" BORDER="0">-Poincaré group implies t
he loss of some of t
he basic properties associated to Feynman
![](/ft/mat/22_00017701/xx<font color=)
large8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s pat
h integral. For instance, loss of t
he group c
haracteristic re
lated to t
he time dependence of t
he evolution operator, or t
he breakdown of t
he composition
law for amplitudes of events occurring successively in time. Additionally some simi
larities between t
he present idea and t
he so called restricted pat
h integral formalism will be underlined. T
hese analogies advocate t
he c
laim t
hat if t
he
![](/ft/mat/22_00017701/xx<font color=)
large954.gif" alt="kappa" align="BASELINE" BORDER="0">-Poincaré group contains some of t
he p
hysical information of t
he quantum gravity vacuum, t
hen t
his vacuum could entail deco
herence. T
his
last result will also allow us to consider t
he possibility of analyzing t
he continuous measurement problem of quantum t
heory from a group-t
heoretical point of view, but now taking into account t
he
![](/ft/mat/22_00017701/xx<font color=)
large954.gif" alt="kappa" align="BASELINE" BORDER="0">-Poincaré symmetries.