Related papers: Path Integral Quantisation of Finite Noncommutativ…
General 2d dilaton theories, containing spherically symmetric gravity and hence the Schwarzschild black hole as a special case, are quantized by an exact path integral of their geometric (Cartan-) variables. Matter, represented by minimally…
For the Jacobian resulting from the previously considered problem of the path integral reduction in Wiener path integrals for a mechanical system with symmetry describing the motion of two interacting scalar particles on a manifold that is…
We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our…
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum…
Using the recently found first order formulation of two-dimensional dilaton gravity with boundary, we perform a Hamiltonian analysis and subsequent path integral quantization. The importance of the boundary terms to obtain the correct…
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…
The gravitational path integral suggests a striking result: the Hilbert space of closed universes in each superselection sector, a so-called $\alpha$-sector, is one-dimensional. We develop an abstract formalism encapsulating recent…
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space…
The spectral triple approach to noncommutative geometry allows one to develop the entire standard model (and supersymmetric extensions) of particle physics from a purely geometry stand point and thus treats both gravity and particle physics…
We review the construction of the path integral and the corresponding effective action for the Regge formulation of General Relativity under the assumption that the short-distance structure of the spacetime is not a smooth 4-manifold, but a…
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the…
This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A $L^2$ Riemannian metric $G_P$ is given on the space of piecewise geodesic paths $H_P(M)$ adapted to…
A distance can be measured by monitoring how much a wheel has rotated when rolled without slipping. This simple idea underlies the mathematics of Cartan geometry. The Cartan-geometric description of gravity consists of a SO(1,4) gauge…
We describe a method to remove non-decoupling heavy fields from a quantized field theory and to construct a low-energy one-loop effective Lagrangian by integrating out the heavy degrees of freedom in the path integral. We apply this method…
We discuss measures on spaces of unparametrized paths related to the Wiener measure. These measures arise naturally in the study of one-dimensional gravity coupled to scalar fields. Two kinds of discrete approximations are defined, the…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…