Related papers: A Straight Forward Path to a Path Integration of E…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
In the first part of this paper I propose the Construction Interpretation of the Quantum. The main point of this interpretation is that (unlike previous interpretations) it is not actually an interpretation but rather a methodology aimed to…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with…
I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k>1. For the Wiener measure…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to…
Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…