Related papers: Finiteness of quantum gravity with matter on a PL …
Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…
We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…
We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in…
We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime…
Gravitational field is the manifestation of space-time translational ($T_4$) gauge symmetry, which enables gravitational interaction to be unified with the strong and the electroweak interactions. Such a total-unified model is based on a…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
I review discrete and continuum approaches to quantized gravity based on the covariant Feynman path integral approach.
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the…
We consider the unitarity of the S-matrix for linearized General Relativity coupled to particle physics models. Taking renormalization group effects of the Planck mass into account, we find that the scale at which unitarity is violated is…
We investigate the requirement of suppressing spacetime geometries with a curvature singularity via destructive interference in the Lorentzian gravitational path integral as a constraint on the microscopic action for gravity. Based on…
We show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open…
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
We consider a class of Schrodinger equations with time-dependent smooth magnetic and electric potentials having a growth at infinity at most linear and quadratic, respectively. We study the convergence in $L^p$ with loss of derivatives,…
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…
In this thesis special emphasis is put on the quantization of the spherically reduced Einstein-massless-Klein-Gordon model using a first order approach for geometric quantities, because phenomenologically it is probably the most relevant of…
In a standard quantum field theory the norm $\langle \Omega\vert \Omega\rangle$ of the vacuum state is taken to be finite. In this paper we provide a procedure, based on constructing an equivalent wave mechanics, for determining whether or…