Electromagnetic and gravitational
interactions of the spinning
particle
Physics Department,
Akdeniz University,
Antalya, TURKEY
• Soon after Einstein proposed his gravitational
theory, Weyl extended it to include
electromagnetism and later revitalized his gauge
idea, U(1) gauge invariance. In 1954, Yang and
Mills generalized U(1) into SU(2). In 1956
Utiyama gauged the Lorentz group, SO(1,3),
and later Kibble extended it into Poincare group,
P .
• Utiyama R 1956, Phys. Rev. 101, 1597.
• Kibble T W B 1961, J. Math. Phys. 2 212.
In most of the gauge theories of
gravitation, P is conceived as the
spacetime symmetry group and the
inner symmetry group which
generate the translations and
Lorentz rotations, and the SO(1, 3)
frame rotations of matter fields,
respectively.
• The global covariance of the matter field
under P, yields the conservation of the
energy-momentum and the total angular
momentum.
In the local extension of the gauge
group P, its spacetime part becomes the
diffeomorphism group, the gauged
theory is invariant under the general
coordinate transformations and the local
SO(1, 3) frame rotations.
In an other approach, P is considered as
the internal symmetry group of matter
fields in Minkowski spacetime to obtain
a complementary gauge formulation of
gravitation and to discuss the
renormalization procedure.
• The Dirac equation is generalized into the
curved spacetime by introducing the Fock
• - Ivananko 2-vector or the spin connection.
• Fock V A 1929 Zeits. Phys. 57 261 and
Fock V A and Ivanenko D D 1929
Comptes Rendus des Seances de
L′Academi des Sciences 188 1470.
• The Dirac algebra relates the metric tensor
of the spacetime to the anti-commutator of
the spacetime dependent Dirac matrices.
In their pioneering investigations,
Schrödinger and Bargmann discussed the
generalization of the spin connection and
showed that it gives the spacetime
curvature, the spin-2 gravitational field,
and an Abelian spin-1 curvature.
• Schrödinger E 1932 Sitz. Preuss. Ak. D. Wiss.