Related papers: Classical and Fluctuating Paths in Spaces with Cur…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
Non-relativistic quantum theory of non-interacting particles in the spacetime containing a region with closed time-like curves (time-machine spacetime) is considered with the help of the path-integral technique. It is argued that, in…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a…
We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…