64
T. K. Mathew
also be modified to fit into the framework of quantum theory and such a unification
is what we called as the quantum gravity. The weak and strong forces were reformulated according to the quantum principles. Because of this, electromagnetic and weak
nuclear interactions are unified within the Standard Model and strong nuclear interaction is currently described by Quantum Chromodynamics. But, classical General
Relativity by Einstein steadily escaped the attempts of quantisation. It is well known
that the problem arises because of the non-renormalizability of General Relativity. It
was shown that General Relativity theory is non-renormalizable after the inclusion
of matter fields. The difficulty with non-renormalizable theories is that they are not
predictive, since to make well-defined predictions it potentially requires an infinite
number of divergent renormalizations.
Another problem is associated with the question of unitarity. According to quantum mechanics, knowledge about the state of a system at one instant is equivalent
to the knowledge about its state at any other instant. This is due to a one-to-one correspondence, between the states at two different instants, induced by the evolution
equations, the Schrodinger equation which is a linear equation. But, the governing
equation in classical gravity is the non-linear field equation, which indicates that the
evolution of a state in gravity may not be unitary. For example, consider a black hole
formed due to the collapse of a star, the resulting configuration is assumed to be a
pure state. But it radiates out completely, leaving behind only the Hawking radiation, which is not a pure state. Such an evolution of a pure state into a mixed state
is not allowed in quantum mechanics. Like this, there arose many barricades like,
positivity, causality, etc., which I am not describing here, for that one may refer to
some standard review article.
3.2 Reformulation of Gravity in Flat Space Using Gauge
Field Theory—A Remarkable Contribution by KBJ
and MS
It is known that the major issue in formulating the quantum version of gravity is
its non-renormalizability. But it was noticed that at least in the currently attainable
energies, gauge field theories are renormalizable. Various attempts have been done
for formulating a gauge field version of Einstein’s gravity. The major huddle is to find
a gauge theoretical formulation of the space–time metric, especially the curvature,
since gauge field theory was formulated in flat space. Attempts were made to gauge
the Lorentz group in a local surrounding and then to transport over to the curved space
manifold to form a gauge theory of gravitation, but it becomes fruitless. A possible
way pointed out is to seek a gauge theoretical reformulation of gravity using YangMills (YM) [1] type of action, because attempt using non-YM action leads to the
undesirable features of non-metricity and torsion.
A major step in reformulating gravity as a gauge theory was done by Dehnen and
Ghaboussi(DG) [2] in 1986, in which the authors created a gauge reformulation of the
T. K. Mathew
also be modified to fit into the framework of quantum theory and such a unification
is what we called as the quantum gravity. The weak and strong forces were reformulated according to the quantum principles. Because of this, electromagnetic and weak
nuclear interactions are unified within the Standard Model and strong nuclear interaction is currently described by Quantum Chromodynamics. But, classical General
Relativity by Einstein steadily escaped the attempts of quantisation. It is well known
that the problem arises because of the non-renormalizability of General Relativity. It
was shown that General Relativity theory is non-renormalizable after the inclusion
of matter fields. The difficulty with non-renormalizable theories is that they are not
predictive, since to make well-defined predictions it potentially requires an infinite
number of divergent renormalizations.
Another problem is associated with the question of unitarity. According to quantum mechanics, knowledge about the state of a system at one instant is equivalent
to the knowledge about its state at any other instant. This is due to a one-to-one correspondence, between the states at two different instants, induced by the evolution
equations, the Schrodinger equation which is a linear equation. But, the governing
equation in classical gravity is the non-linear field equation, which indicates that the
evolution of a state in gravity may not be unitary. For example, consider a black hole
formed due to the collapse of a star, the resulting configuration is assumed to be a
pure state. But it radiates out completely, leaving behind only the Hawking radiation, which is not a pure state. Such an evolution of a pure state into a mixed state
is not allowed in quantum mechanics. Like this, there arose many barricades like,
positivity, causality, etc., which I am not describing here, for that one may refer to
some standard review article.
3.2 Reformulation of Gravity in Flat Space Using Gauge
Field Theory—A Remarkable Contribution by KBJ
and MS
It is known that the major issue in formulating the quantum version of gravity is
its non-renormalizability. But it was noticed that at least in the currently attainable
energies, gauge field theories are renormalizable. Various attempts have been done
for formulating a gauge field version of Einstein’s gravity. The major huddle is to find
a gauge theoretical formulation of the space–time metric, especially the curvature,
since gauge field theory was formulated in flat space. Attempts were made to gauge
the Lorentz group in a local surrounding and then to transport over to the curved space
manifold to form a gauge theory of gravitation, but it becomes fruitless. A possible
way pointed out is to seek a gauge theoretical reformulation of gravity using YangMills (YM) [1] type of action, because attempt using non-YM action leads to the
undesirable features of non-metricity and torsion.
A major step in reformulating gravity as a gauge theory was done by Dehnen and
Ghaboussi(DG) [2] in 1986, in which the authors created a gauge reformulation of the