Related papers: Quantum Phase Space from String Solitons
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…
In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Recently, a correspondence has been shown to exist between the structure of a single Standard Model generation of elementary particles and the properties of the Clifford algebra of nonrelativistic phase space. Here, this correspondence is…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
In this article we consider quantum phase space reduction when zero is a regular value of the momentum map. By analogy with the classical case we define the BRST cohomology in the framework of deformation quantization. We compute the…
A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is…
The discrete phase space and continuous time representation of relativistic quantum mechanics is further investigated here as a continuation of paper I [1]. The main mathematical construct used here will be that of an area-filling Peano…
We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely…
We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM…
We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors…
We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…
The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously as one changes the vacuum on the Coulomb branch of gauge theories with extended supersymmetry in four dimensions. We show that…
Electromagnetic modes are instrumental in building quantum machines. In this experiment, we introduce a method to manipulate these modes by effectively controlling their phase space. Preventing access to a single energy level, corresponding…
We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future)…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
The discovery by Tranquada et al. of an ordered phase of charged domain walls in the high-Tc cuprates leads us to consider the possible existence of a quantum domain-wall liquid. We propose minimal models for the quantization, by meandering…
Within a Liouville approach to non-critical string theory, we argue for a non-trivial commutation relation between space and time observables, leading to a non-zero space-time uncertainty relation $\delta x \delta t > 0$, which vanishes in…