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Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…
The method of the real time perturbative calculations of nonequilibrium averages is generalised to the case of varying chemical potential. Calculations are performed in the frame of Zubarev's nonequilibrium density matrix approach. In this…
We consider a one-dimensional optical lattice of three-dimensional Harmonic Oscillators which are loaded with neutral fermionic atoms trapped into two hyperfine states. By means of a standard variational coherent-state procedure, we derive…
The techniques employed to solve the interaction of a detector and a quantum field typically require perturbation methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with…
This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a…
We present the so-called Liouville-Neumann (LN) approach to nonequilibrium quantum fields. The LN approach unifies the functional Schr\"{o}dinger equation and the LN equation for time-independent or time-dependent quantum systems and for…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
There is no relativistic Hamiltonian for many particles systems except for free particles and this has been accepted since the 1960s from the work of Currie, Jordan and Sudarshan, Cannon and Jordan, and Leutwyler. This is the problem we…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be…
In quantum field theory, elemental particles are assumed to be point particles. As a result, the loop integrals are divergent in many cases. Regularization and renormalization are necessary in order to get the physical finite results from…
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…
Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincare group only the Hamiltonian and the boost operators carry interactions, we offer an…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups.…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…