相关论文: Inequivalent Quantization in the Skyrme Model

The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…

The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the…

A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of…

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models…

The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…

It is shown, that the space quantum existence (SQE)non-ambigously determine the metric form for the space without time, using weak condition of metrics addivity. The hypotesis is proposed, Riemann metics is only possible for quantized space…

We show that the rational Calogero model with suitable boundary condition admits quantum states with non-equispaced energy levels. Such a spectrum generically consists of infinitely many positive energy states and a single negative energy…

The "quantum-event / prime ideal in a category/ noncommutative-point" alternative to "classical-event / commutative prime ideal/ point" is suggested. Ideals in additive categories, prime spectra and representation of quivers are considered…

It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…

Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of…

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order…

There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…

The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…

We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…

We derive finite-dimensional quantum mechanics from a single ontological principle, that \emph{existence is constituted by distinguishability}, together with two structural commitments: finite capacity $N$ (parametric input) and…

Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…

Collective modes of interacting many-body systems can be related to the motion on classically invariant manifolds. We introduce suitable coordinate systems. These coordinates are Cartesian in position and momentum space. They are collective…