Related papers: Covariant integral quantization of the unit disk
We carry out the canonical analysis of a covariant version of unimodular gravity in terms of the connection representation. We then proceed to quantize this theory by implementing the Dirac procedure. We confirm whether and how the Kodama…
We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal…
Nonlinear interferometers are promising tools for quantum metrology, as they are characterized by an improved phase sensitivity scaling compared to linear interferometers operating with classical light. However, the multimodeness of the…
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an…
Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $d^{p+q}$-dimensional matrix variable that…
In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field.…
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…
The problem of quantizing the canonical pair angle and action variables phi and I is almost as old as quantum mechanics itself and since decades a strongly debated but still unresolved issue in quantum optics. The present paper proposes a…
By performing two local displacement operations (LDOs) inside an SU(1,1) interferometer, called as the displacement-assisted SU(1,1) [DSU(1,1)], both the phase sensitivity based on homodyne detection and quantum Fisher information (QFI)…
We theoretically study the quantum Fisher information (QFI) of the SU(1,1) interferometer with phase shifts in two arms taking account of realistic noise effects. A generalized phase transform including the phase diffusion effect is…
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
We discuss various aspects of positive kernel method of quantization of the one-parameter groups $\tau_t \in \mbox{Aut}(P,\vartheta)$ of automorphisms of a $G$-principal bundle $P(G,\pi,M)$ with a fixed connection form $\vartheta$ on its…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…
We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of…
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states…
We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible…
We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…