Related papers: Simplification of nonlinear equations for a field …
In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy…
The spinless Salpeter equation represents the simplest and most straightforward generalization of the Schroedinger equation of standard nonrelativistic quantum theory towards the inclusion of relativistic kinematics. Moreover, it can be…
We study the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field theory version of…
We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of…
For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…
A generic theory of a single real scalar field is considered, and a simple method is presented for obtaining a class of solutions to the equation of motion. These solutions are obtained from a simpler equation of motion that is generated by…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
We discuss the quantum action principles and equations of motion for Heavy Quark Effective Field Theory. We prove the so-called equivalence theorem for HQEFT which states that the physical predictions of HQEFT are independent from the…
Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we…
The unified field is a Maxwell-Lorentz field. Maxwell-Lorentz equations for potentials in standard four-dimensional form are satisfied exactly. This is achieved by involving new fundamental field sources, strict definition of which requires…
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…
In this letter, we show how one can solve easily the Potts-3 + branching interactions and Potts-\infty matrix models, by the means of the equations of motion (loop equations). We give an algebraic equation for the resolvents of these…
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a…
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the…
Single scale Feynman integrals in quantum field theories obey difference or differential equations with respect to their discrete parameter $N$ or continuous parameter $x$. The analysis of these equations reveals to which order they…
In the framework of bulk reconstruction, we elucidate the relationship between the action of CFT modular Hamiltonians on bulk operators, the possible equation of motion for the bulk operators, and the charge distribution at infinity…
We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where…
We develop a method for the simulation of scalar field theories with complex actions which is local, simple to implement and can be used in any number of space-time dimensions. For model systems satisfying the $\mathcal{PT}$ symmetry…
In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…