Related papers: Path integrals, spontaneous localisation, and the …
The paper is devoted to some of the difficulties which the Wheeler - DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We construct a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. To the best of our knowledge this is the first rigorous construction of such an object and this is…
We consider the Grover walk on infinite trees from the view point of spectral analysis. From the previous works, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of…
Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the…
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…
Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic…
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…
Based on a generalization of the stochastic quantization scheme recently a modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory was derived, the modification consisting in the presence of specific finite…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given…
We investigate the classical and quantum dynamics of $f(R)$ gravity's rainbow in the presence of a perfect fluid, employing Schutz's formalism to establish a well-defined notion of time. In the classical regime, we derive and solve the…
I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and…
We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power…
A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the…
In this paper an overview of some recent developments on the classical limit and spontaneous symmetry breaking (SSB) in algebraic quantum theory is given. In such works, based on the theory of $C^*$-algebras, the concept of the classical…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…