Related papers: Path integral duality modified propagators in spac…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
The aim of this paper is to associate a measure for certain sets of paths in the Euclidean plane $\mathbb{R}^2$ with fixed starting and ending points. Then, working on parameterized surfaces with a specific Riemannian metric, we define and…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale $\cal L$ much greater than Planck length $\ell_P=1.2\times 10^{-33}$cm, a spin-1/2 field in flat spacetime.…
We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity.…
The basic properties of Poincare gauge invariant Hilbert bundles over Lorentzian manifolds are derived. Quantum connections are introduced in such bundles, which govern a parallel transport that is shown to satisfy the strong equivalence…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature 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…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is…
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…
Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation…
Electromagnetic interactions of the spin 3/2 particle are investigated while allowing the propagation of the transverse spin 1/2 component present in the reducible Rarita-Schwinger vector-spinor. This is done by allowing a more general form…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex…
The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe…
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and…
We discuss a path integral formalism to introduce noncommutative generalizations of spacetime manifold in even dimensions, which have been suggested to be reasonable effective pictures at very small length scales, of the order of Planck…