相关论文: How to Quantize Phases and Moduli!
The problem of determining the pion electromagnetic formfactor $F(q^2)$ in the space-like region from the value of its modulus in the time-like region is solved by the formfactor analyticity. If $F(q^2)$has no zeroes in the complex plane…
It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have…
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…
We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\tfrac{1}{2}$ systems. We develop a…
A symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model for the entire range of parameters and obtain…
We compare the usual operator modulus with two symmetrized variants, the arithmetic symmetric modulus and the quadratic symmetric modulus. For every unitarily invariant norm, we determine sharp equivalence constants among these three…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
We introduce a quantification of genuine three-party pure-state coherence for wave fields, classical and quantum, by borrowing concepts from classical optics. The tensor structure of a classical paraxial light beam composed of three…
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two…
The moduli space of spatial polygons is known as a symplectic manifold equipped with both K\"ahler and real polarizations. In this paper, associated to the K\"ahler and real polarizations, morphisms of operads…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define…
Starting with a previously constructed family of coherent states, we introduce the Berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural Poisson algebra. The…
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schr\"odinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum…
We present a statistical model of non-interacting individual classical particles that may lead to a microscopic implementation of quantum mechanics. The model requires the action of a special type of detector that detects and records…
We develop a classical picture of interference for non-interacting individual classical massive free particles. As long as they remain undetected, particles carry the information of a phase equal to an action integral along their…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…