Related papers: Quantum gravitational corrections to propagator in…
We present a general relativistic framework for studying gravitational effects in quantum mechanical phenomena. We concentrate our attention on the case of ultra-relativistic, spin-1/2 particles propagating in Kerr spacetime. The…
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…
In the effective field theory approach to gravity, the Lagrangian density for general relativity is supplemented by generally covariant terms of higher order in the Riemann tensor and its derivatives. At face value, these terms will result…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
We examine the corrections to the lowest order gravitational interactions of massive particles arising from gravitational radiative corrections. We show how the masslessness of the graviton and the gravitational self interactions imply the…
We derive the Feynman rules for the graviton in the presence of a flat Robertson-Walker background and give explicit expressions for the propagator in the physically interesting cases of inflation, radiation domination, and matter…
Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do…
The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure $N(x_2,x_1;\sigma)$ for the effective number…
We suggest to use "minimal" choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Riemannian space and metric (or vierbein field) is the dynamical variable. We then suggest to use the simplest…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
In previous work, a lattice scalar propagator was rigorously defined in $d=1$ flat space and shown to equal the known Klein-Gordon propagator of QFT. This work generalizes this lattice propagator to manifolds whose universal cover is the…
It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on…
The usual (Bunch-Davies) Feynman propagator of a massless field is not well defined in an expanding universe due to the presence of infrared divergences. We propose a new propagator which yields infrared finite answers to any correlation…
We compute the one-loop quantum corrections to the gravitational potentials of a spinning point particle in a de Sitter background, due to the vacuum polarisation induced by conformal fields in an effective field theory approach. We…
we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the $L^2$ transition probability amplitude via…
We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the na\"ive continuum limit but which, nevertheless, induce non-trivial effects due to quantum…
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…
We study the graviton propagator in euclidean loop quantum gravity, using the spinfoam formalism. We use boundary-amplitude and group-field-theory techniques, and compute one component of the propagator to first order, under a number of…
Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting…