Related papers: Quantum curves as quantum distributions
We develop a quantum circuit model describing unitary interactions between quantum fields and a uniformly accelerated object, and apply it to a semi-transparent mirror which uniformly accelerates in the Minkowski vacuum. The reflection…
We describe the quantum phase transition of a Fermi gas occurring when the quasiparticle excitation energy has a minimum in momentum space which crosses zero on a sphere of radius k_0 \neq 0. The quasiparticles have a universal interaction…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…
We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…
In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum…
The evolution of an initially smooth spatial inhomogeneity in the density of a one-dimensional Fermi gas is well described by classical mechanics. The classical evolution leads to the formation of a shock wave: the density develops kinks in…
The classical limit problem of quantum mechanics is revisited on the basis of a scheme that enables a quantitative study of the way the quantum-classical agreement emerges while going through the intermediate mass range between the…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with…
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ…
Motivated by applications in background-independent quantum gravity, we discuss the quantization of labeled and unlabeled finite multigraphs with a maximum edge count. We provide a unified way to represent quantum multigraphs with labeled…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…