Related papers: Schwinger, Pegg and Barnett approaches and a relat…

Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of…

We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…

In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which…

We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $\pi^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to…

The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe…

Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions--the density matrices in phase-space…

We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…

We consider the world-line quantisation of a system invariant under the symmetries of reciprocal relativity. Imposition of the first class constraint, the generator of local time reparametrisations, on physical states enforces…

The concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…

The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. The formalism is developed to account for dynamical processes, with or…

Perturbative expansions for atoms in QED are developed around interacting states, typically defined by the Schr\"odinger equation. Calculations are nevertheless done using the standard Feynman diagram expansion around free states. The…

We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the…

In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and…

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…

This explanatory note, based on the geometrical method by Kijovski and Tulczyjew, describes the construction of the reduced phase space of Lagrangian field theories, i.e., the correct space of initial conditions with its symplectic…

In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…

Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice ${\ee Z}_{D} \times {\ee Z}_{D}$ with specific emphasis on the deformed oscillator subalgebras and the generalized representations…

We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum…

We compare the Pegg-Barnett (PB) formalism with the covariant phase observable approach to the problem of quantum phase and show that PB-formalism gives essentially the same results as the canonical (covariant) phase observable. We also…