相关论文: Quantization of symplectic dynamical r-matrices an…

In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions naturally appear in this setting. As an application, we use a…

We present a method where derivations of star-product algebras are used to build covariant derivatives for noncommutative gauge theory. We write down a noncommutative action by linking these derivations to a frame field induced by a…

We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…

We study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong…

This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice…

Characterizing quantum dynamics is essential for quantifying arbitrary properties of a quantum process -- such as its ability to exhibit quantum-mechanical dynamics or generate entanglement. However, current methods require a number of…

It is shown that the wave function describing the pure state of a single-particle quantum ensemble, in addition to statistical restrictions, imposes restrictions on the particle momentum at points in the configuration space $\mathbb{R}^3$:…

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…

We construct finite $R$-matrices for the first fundamental representation $V$ of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ for classical $\mathfrak{g}$, both through the decomposition of $V\otimes V$ into irreducibles…

We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that…

Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…

There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical…

The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…

The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…

We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in…

We formulate an equivalence between the 2-dim $\sigma$-model spectrum expanded on a non-trivial massive vacuum and a classical particle Hamiltonian with variable mass and potential. By considering methods of analytic Galoisian…

R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov…