Related papers: Fuzzy spheres from inequivalent coherent states qu…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
On the fuzzy sphere, no state saturates simultaneously all the Heisenberg uncertainties. We propose a weaker uncertainty for which this holds. The family of states so obtained is physically motivated because it encodes information about…
We analyze mathematical and physical properties of a previously introduced [J. Phys. A47, 115302 (2014)] family of $U(4)$ coherent states (CS). They constitute a matrix version of standard spin $U(2)$ CS when we add an extra (pseudospin)…
By making the second quantization for the Cini Model of quantum measurement without wave function collapse [M. Cini, Nuovo Cimento, B73 27(1983)], the second order quantum decoherence (SOQD) is studied with a two mode boson system…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…
We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two…
This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to the condensed matter physics, which obeys a $f$-deformed…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
We examine the L\"uscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total…
In conformal field theory (CFT), the four-point correlator is a fundamental object that encodes CFT properties, constrains CFT structures, and connects to the gravitational scattering amplitude in holography theory. However, the four-point…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study,…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional(2D) magnetic scalar and three-dimensional(3D) electric and magnetic scalars. We discuss two different quantization schemes, depending…