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We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given…
Maxwell theory can be studied in a gauge which is invariant under conformal rescalings of the metric, and first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean 4-space. The resulting…
The purely mathematical root of the dequantization constructions is the quest for a sheafification needed for presheaves on a noncommutative space. The moment space is constructed as a commutative space, approximating the noncommutative…
We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the…
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of…
We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative…
We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation…
Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators,…
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a…
We propose a notion of functor of points for noncommutative spaces, valued in categories of bimodules, and endowed with an action functional determined by a notion of hermitian structures and height functions, modeled on an interpretation…
The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter…
The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
Coordinate noncommutativity, rather than being introduced through deformations of operator products, is achieved by coupling an auxiliary system with large energy excitations to the one of interest. Integrating out the auxiliary dynamics,…
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed…
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM)…