Related papers: Quantum "Twin Peaks" or Path Integrals in the Futu…
A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…
Quantum Poincar\'e-Weyl group in two dimensional quantum Minkowski space-time is considered and an appriopriate relativistic kinematics is investigated. It is claimed that a consistent approach to the above questions demands a kind of a…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
We introduce a gauge and diffeomorphism invariant theory on Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric…
A space-time symmetric and explicitly Lorentz covariant path integral formalism of relativistic quantum mechanics is proposed, which produces partial locally correlations of quantum processes of massive particles with the velocity of light…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
A brief review of a self-contained genuinely three-dimensional monodromy-matrix based non-perturbative covariant path-integral approach to {\it polynomial invariants} of knots and links in the framework of (topological) quantum Chern-Simons…
The Kreck-Stolz $s$-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
We investigate equivariant analogues of the Minkowski--Weyl theorem and Gordan's lemma in an infinite-dimensional setting, where cones and monoids are invariant under the action of the infinite symmetric group. Building upon the framework…
We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair…
We propose a theory of quantum gravity which formulates the quantum theory as a nonperturbative path integral, where each spacetime history appears with a weight given by the exponentiated Einstein-Hilbert action of the corresponding causal…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
The role of a physical phase space structure in a classical and quantum dynamics of gauge theories is emphasized. In particular, the gauge orbit space of Yang-Mills theories on a cylindrical spacetime (space is compactified to a circle) is…