  In this thesis we consider the problem of dynamics in canonical loop quantum
gravity, primarily in the context of deparametrized models, in which a scalar
field is taken as a physical time variable for the dynamics of the
gravitational field. The dynamics of the quantum states of the gravitational
field is then generated directly by a physical Hamiltonian operator, instead of
being implicitly defined through the kernel of a Hamiltonian constraint.
  We introduce a new construction of a Hamiltonian operator for loop quantum
gravity, which has both mathematical and practical advantages in comparison to
earlier proposals. Most importantly, the new Hamiltonian can be constructed as
a symmetric operator, and is therefore a mathematically consistent candidate
for a generator of physical time evolution in deparametrized models. We develop
methods for approximately evaluating the dynamics generated by a given physical
Hamiltonian, even if an exact solution to the eigenvalue problem of the
Hamiltonian cannot be achieved. We also introduce a new representation for
intertwiners in loop quantum gravity, based on projecting intertwiners onto
coherent states of angular momentum, and in which intertwiners are represented
as polynomials of certain complex variables, and operators in loop quantum
gravity are expressed as differential operators acting on these variables.
  In addition to reviewing the results of the author's scientific work, this
thesis also gives a thorough introduction to the basic framework of canonical
loop quantum gravity, and a self-contained presentation of the graphical
formalism for SU(2) recoupling theory, which is the invaluable tool for
performing practical calculations in loop quantum gravity. The author therefore
hopes that parts of this thesis could serve as a comprehensible source of
information for anyone interested in learning the elements of loop quantum
gravity.
