Related papers: Phase space formalisms of quantum mechanics with s…
Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of…
The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be…
Starting from the canonical phase space for discretised (4d) BF-theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces.…
In this paper a system-oriented formalism of Quantum Information Processing is presented. Its form resembles that of standard signal processing, although further complexity is added in order to describe pure quantum-mechanical effects and…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The…