Related papers: Quantum gravitational corrections to propagator in…
The action for a relativistic free particle of mass $m$ receives a contribution $-mds$ from a path segment of infinitesimal length $ds$. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of…
In the path integral expression for a Feynman propagator of a spinless particle of mass $m$, the path integral amplitude for a path of proper length ${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetime described by the…
The existence of a minimal and fundamental length scale, say, the Planck length, is a characteristic feature of almost all the models of quantum gravity. The presence of the fundamental length is expected to lead to an improved ultra-violet…
Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include…
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length,…
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in $\mathbb{R}^D$ are shown to be the result of summing over all dimensions $D'\geq D$ of $\mathbb{R}^{D'}$, each summand…
Following the idea of Alekseev and Shatashvili we derive the path integral quantization of a modified relativistic particle action that results in the Feynman propagator of a free field with arbitrary spin. This propagator can be associated…
We propose to include gravity in quantum field theory non-perturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the four-momenta of the other particles in the same…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
The (Feynman) propagator $G(x_2,x_1)$ encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator -- either as a time ordered correlator or from…
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may…
It has been often conjectured that the correct theory of quantum gravity will act as a UV regulator in the low energy limit of quantum field theory. Earlier work has shown that if the path integral defining the quantum field theory…
We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…
The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of the gauge theory to simplify the quasiclassical propagator. The latter is achieved due to a specific…
We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time…
We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian…
The canonical approach to quantizing quantum gravity is understood to suffer from pathological non-renomalizability. Nevertheless in the context of effective field theory, a viable perturbative approach to calculating elementary processes…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
Power duality in Feynman's path integral formulation of quantum mechanics is investigated. The power duality transformation consists of a change in coordinate and time variables, an exchange of energy and coupling, and a classical angular…