Related papers: Dynamical mapping method in nonrelativistic models…
We derive the renormalized nonequilibrium equations of motion for a scalar field and its quantum back reaction in a conformally flat Friedmann-Robertson-Walker universe. We use a fully covariant formalism proposed by us recently for…
The so-called equation of motion method is useful to obtain the explicit form of the eigenvectors and eigenvalues of certain non self-adjoint bosonic Hamiltonians with real eigenvalues. These operators can be diagonalized when they are…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
We investigate the dynamics of the driven Jaynes-Cummings model, where a two-level atom interacts with a quantized field and both, atom and field, are driven by an external classical field. Via an invariant approach, we are able to…
Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…
A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed. The infinite hierarchy of quantum conservation laws and…
The D=0 matrix model is reformulated as a 2d nonlocal quantum field theory. The interactions occur on the one-dimensional line of hermitian matrix eigenvalues. The field is conjugate to the density of matrix eigenvalues which appears in the…
In order to find reliable and efficient numerical approximation schemes, we suggest to identify the Functional Renormalization Group flow equations of one-particle irreducible two-point functions as Hamilton-Jacobi(-Bellman)-type partial…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
A new one-dimensional fermion model depending on two independent interaction parameters is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian of the model contains the Hubbard interaction and correlated hopping as…
We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…