scholarly journals Variational wave equations of two fermions interacting via scalar, pseudoscalar, vector, pseudovector and tensor fields

Open Physics ◽  
2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Askold Duviryak ◽  
Jurij Darewych
Keyword(s):  
Wave Equations ◽  
Body Wave ◽  
Vacuum State ◽  
Nonlocal Interaction ◽  
Tensor Fields ◽  
Tensor Coupling ◽  
Coordinate Representation ◽  
Interaction Terms ◽  
Breit Equation ◽  
Variational Wave

AbstractWe consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.

Variational wave equations for relativistic few-body systems in QFT

2006 ◽  
Vol 84 (6-7) ◽  
pp. 625-632 ◽  
Author(s):  
J W Darewych
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Wave Equations ◽  
Body Wave ◽  
Hamiltonian Formalism ◽  
Approximate Solutions ◽  
Quantum Field ◽  
Fermion Fields ◽  
Variational Wave ◽  
03.65 Ge

The variational method in a reformulated Hamiltonian formalism of quantum field theory is used to derive relativistic few-body wave equations for scalar and Fermion fields. Analytic and approximate solutions of some two-body bound states are presented.PACS Nos.: 03.65.Pm, 03.65.Ge, 03.70.+k, 11.10.Ef, 11.10.St, 11.15.Tk, 36.10.Dr

Flux-normalized wavefield decomposition and migration of seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. S83-S92 ◽  
Author(s):  
Bjørge Ursin ◽  
Ørjan Pedersen ◽  
Børge Arntsen
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Transmission Loss ◽  
Correction Term ◽  
Eigenvalue Decomposition ◽  
System Matrix ◽  
Interaction Terms ◽  
Reflectivity Function ◽  
And Migration ◽  
Wavefield Decomposition

Separation of wavefields into directional components can be accomplished by an eigenvalue decomposition of the accompanying system matrix. In conventional pressure-normalized wavefield decomposition, the resulting one-way wave equations contain an interaction term which depends on the reflectivity function. Applying directional wavefield decomposition using flux-normalized eigenvalue decomposition, and disregarding interaction between up- and downgoing wavefields, these interaction terms were absent. By also applying a correction term for transmission loss, the result was an improved estimate of the up- and downgoing wavefields. In the wave equation angle transform, a crosscorrelation function in local offset coordinates was Fourier-transformed to produce an estimate of reflectivity as a function of slowness or angle. We normalized this wave equation angle transform with an estimate of the plane-wave reflection coefficient. The flux-normalized one-way wave-propagation scheme was applied to imaging and to the normalized wave equation angle-transform on synthetic and field data; this proved the effectiveness of the new methods.

scholarly journals SINGULARITY-FREE BREIT EQUATION FROM CONSTRAINT TWO-BODY DIRAC EQUATIONS

1996 ◽  
Vol 05 (04) ◽  
pp. 589-615 ◽  
Author(s):  
HORACE W. CRATER ◽  
CHUN WA WONG ◽  
CHEUK-YIN WONG
Keyword(s):  
Quantum Electrodynamics ◽  
Bound States ◽  
Two Body Problem ◽  
Dirac Equations ◽  
Coupled Equations ◽  
Interaction Terms ◽  
Potential Form ◽  
Orthogonality Constraint ◽  
Hyperbolic Form ◽  
Breit Equation

We examine the relation between two approaches to the quantum relativistic two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations derived from constraint dynamics. In applications to quantum electrodynamics, the former equation becomes pathological if certain interaction terms are not treated as perturbations. The difficulty comes from singularities which appear at finite separations r in the reduced set of coupled equations for attractive potentials even when the potentials themselves are not singular there. They are known to give rise to unphysical bound states and resonances. In contrast, the two-body Dirac equations of constraint dynamics do not have these pathologies in many nonperturbative treatments. To understand these marked differences we first express these contraint equations, which have an “external potential” form, similar to coupled one-body Dirac equations, in a hyperbolic form. These coupled equations are then recast into two equivalent equations: (1) a covariant Breit-like equation with potentials that are exponential functions of certain “generator” functions, and (2) a covariant orthogonality constraint on the relative momentum. This reduction enables us to show in a transparent way that finite-r singularities do not appear as long as the exponential structure is not tampered with and the exponential generators of the interaction are themselves nonsingular for finite r. These Dirac or Breit equations, free of the structural singularities which plague the usual Breit equation, can then be used safely under all circumstances, encompassing numerous applications in the fields of particle, nuclear, and atomic physics which involve highly relativistic and strong binding configurations.

scholarly journals Two‐body wave equations in curved space–time

1996 ◽  
Vol 37 (9) ◽  
pp. 4274-4291 ◽  
Author(s):  
Philippe Droz‐Vincent
Keyword(s):  
Wave Equations ◽  
Body Wave ◽  
Space Time ◽  
Curved Space

scholarly journals The Bargmann-Wigner equations in spherical space

2006 ◽  
Vol 84 (1) ◽  
pp. 37-52
Author(s):  
D.G.C. McKeon ◽  
T N Sherry
Keyword(s):  
Gauge Invariance ◽  
Wave Equations ◽  
Antisymmetric Tensor ◽  
Spherical Space ◽  
Point Function ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Spherical Surfaces ◽  
The One

The Bargmann–Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.PACS No.: 11.30–j

scholarly journals Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 101 ◽  
Author(s):  
Kalyan Manna ◽  
Vitaly Volpert ◽  
Malay Banerjee
Keyword(s):  
Prey Species ◽  
Population Distribution ◽  
Chaotic Oscillation ◽  
Turing Instability ◽  
Transient Dynamics ◽  
Nonlocal Interaction ◽  
Interaction Terms ◽  
Population Distributions ◽  
Predator Model ◽  
Spatiotemporal Models

Investigation of interacting populations is an active area of research, and various modeling approaches have been adopted to describe their dynamics. Mathematical models of such interactions using differential equations are capable to mimic the stationary and oscillating (regular or irregular) population distributions. Recently, some researchers have paid their attention to explain the consequences of transient dynamics of population density (especially the long transients) and able to capture such behaviors with simple models. Existence of multiple stationary patches and settlement to a stable distribution after a long quasi-stable transient dynamics can be explained by spatiotemporal models with nonlocal interaction terms. However, the studies of such interesting phenomena for three interacting species are not abundant in literature. Motivated by these facts here we have considered a three species prey–predator model where the predator is generalist in nature as it survives on two prey species. Nonlocalities are introduced in the intra-specific competition terms for the two prey species in order to model the accessibility of nearby resources. Using linear analysis, we have derived the Turing instability conditions for both the spatiotemporal models with and without nonlocal interactions. Validation of such conditions indicates the possibility of existence of stationary spatially heterogeneous distributions for all the three species. Existence of long transient dynamics has been presented under certain parametric domain. Exhaustive numerical simulations reveal various scenarios of stabilization of population distribution due to the presence of nonlocal intra-specific competition for the two prey species. Chaotic oscillation exhibited by the temporal model is significantly suppressed when the populations are allowed to move over their habitat and prey species can access the nearby resources.

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