Related papers: Quantum curves as quantum distributions
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Zero temperature states of matter are holographically described by a spacetime with an asymptotic electric flux. This flux can be sourced either by explicit charged matter fields in the bulk, by an extremal black hole horizon, or by a…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…
In this job, we will present a theory called Quantum Tomography that is the natural extension of the theory of detection of signals in classical telecommunications to Quantum Mechanics. This theory mainly consists in the reconstruction of a…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the vector representation are constructed. The quantum moduli spaces…
We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition…
A class of models is considered for a quantum particle constrained on degenerate Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the underlying geometry: the corresponding spectral analysis is developed in…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
An emissivity formula is derived using the generalised Fermi-Weizacker-Williams method of virtual photons which accounts for the recoil the charged particle experiences as it emits radiation. It is found that through this derivation the…