NEW INSIGHTS IN PARTICLE DYNAMICS
 FROM GROUP COHOMOLOGY

Work partially supported by DGICYT

V. Aldaya $^{a,b}$, J. L. Jaramillo $^{a,b}$, J. Guerrero $^{a,b,c}$
$^a$ Instituto de Astrof\'{\i}sica de Andaluc\'{\i}a, 
Granada, Spain

$^b$ Instituto de F\'{\i}sica Te\'{o}rica y Computacional Carlos I, Facultad de Ciencias, 

Universidad de Granada, Granada, Spain

$^c$ Departamento de Matem\'{a}tica Aplicada, Facultad de 
Inform\'{a}tica, Murcia, Spain

The dynamics of a particle, moving in background 
electromagnetic and gravitational fields, is revisited from a Lie 
group cohomological perspective. Physical constants characterising the 
particle appear as central extension parameters of a group which is obtained 
from a previously extended kinematical group (Poincar\'e or Galilei) by 
making  local some subgroup. The corresponding dynamics is generated by a
vector field inside the kernel of a presymplectic form, which is derived from
the canonical left-invariant one-form on the extended group.  The 
nonrelativistic (Newtonian) limit is derived from the geodesic motion 
via an In\"on\"u--Wigner contraction. A deeper analysis of the 
cohomological structure reveals the possibility of a new force associated with
a nontrivial mixing of gravity and electromagnetism leading to testable 
predictions, such as a mass difference between charged particles and 
antiparticles.