Related papers: Path Sums for Propagators in Causal Sets
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
The propagator of a scalar field on a stationary slowly varying in space gravitational background is derived retaining only the second derivatives of the metric. The corresponding one-loop effective action is constructed. The propagator and…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
In this comment it is pointed out that the perturbative dynamics of general massive field theories can be mapped to delimited sums of determined integral functions. The limits on the sums are the remaining obstacle to finding the general…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the…
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the…
This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains…
Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations,…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
The Feynman propagator for a free bosonic scalar field on the discrete spacetime of a causal set is presented. The formalism includes scalar field operators and a vacuum state which define a scalar quantum field theory on a causal set. This…
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 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,…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via…
By appeal to Distribution Theory we discuss in rigorous fashion, without appealing to {\bf any conjecture} (as usually done by other authors), the boundary-bulk propagators for the scalar field, both in the non-massive and massive cases.…