相关论文: Multi-Matrix Quantum Mechanics, Collective Fields …

Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…

Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…

The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is…

We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the…

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized…

Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.

The eletromagnetic field in a linear absorptive dielectric medium, is quantized in the framework of the damped polarization model. A Hamiltonian containing a reservoir with continuous degrees of freedom, is proposed. The reservoir minimally…

We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…

Spatially homogeneous field theories are studied in the framework of dynamical system theory. In particular we consider a model of inflationary cosmology and a Yang-Mills-Higgs system. We discuss also the role of quantum chaos and its…

Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing light-front gauge and adopting a basis function…

We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in…

Several reductions of the bosonic BMN matrix model equations to ordinary point particle Hamiltonian dynamics in the plane (or R^3) are given - as well as a few explicit solutions (some of which, as N->infinity, correspond to membranes…

The work contains a detailed investigation of free neutral (Hermitian) or charged (non-Hermitian) scalar fields and the describing them (system of) Klein-Gordon equation(s) in momentum picture of motion. A form of the field equation(s) in…

We study the formulation of quantum statistical mechanics in noncommutative spaces. We construct microcanonical and canonical ensemble theory in noncommutative spaces. We consider for illustration some basic and important examples in the…

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the…

In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…

In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present…

The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…