735 research outputs found
Cross-ladder effects in Bethe-Salpeter and Light-Front equations
Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is
solved for a kernel given by a sum of ladder and cross-ladder exchanges. The
solution of corresponding Light-Front (LF) equation, where we add the
time-ordered stretched boxes, is also obtained. Cross-ladder contributions are
found to be very large and attractive, whereas the influence of stretched boxes
is negligible. Both approaches -- BS and LF -- give very close results.Comment: 11 pages, 7 figure
Solving Bethe-Salpeter equation in Minkowski space
We develop a new method of solving Bethe-Salpeter (BS) equation in Minkowski
space. It is based on projecting the BS equation on the light-front (LF) plane
and on the Nakanishi integral representation of the BS amplitude. This method
is valid for any kernel given by the irreducible Feynman graphs. For massless
ladder exchange, our approach reproduces analytically the Wick-Cutkosky
equation. For massive ladder exchange, the numerical results coincide with the
ones obtained by Wick rotation.Comment: 10 pages, 4 figure
Deduction with XOR Constraints in Security API Modelling
We introduce XOR constraints, and show how they enable a theorem prover to reason effectively about security critical subsystems which employ bitwise XOR. Our primary case study is the API of the IBM 4758 hardware security module. We also show how our technique can be applied to standard security protocols
Exact spinor-scalar bound states in a QFT with scalar interactions
We study two-particle systems in a model quantum field theory, in which
scalar particles and spinor particles interact via a mediating scalar field.
The Lagrangian of the model is reformulated by using covariant Green's
functions to solve for the mediating field in terms of the particle fields.
This results in a Hamiltonian in which the mediating-field propagator appears
directly in the interaction term. It is shown that exact two-particle
eigenstates of the Hamiltonian can be determined. The resulting relativistic
fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle
limits. Analytic solutions for the bound state energy spectrum are obtained for
the case of massless mediating fields.Comment: 12 pages, RevTeX, 1 figur
Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
The Bethe-Salpeter equation for Wick-Cutkosky like models is solved in
dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger
equations for propagators is combined with the dressed ladder Bethe-Salpeter
equation for the scalar S-wave bound state amplitudes. With the help of
spectral representation the results are obtained directly in Minkowski space.
We give a new analytic formula for the resulting equation simplifying the
numerical treatment. The bare ladder approximation of Bethe-Salpeter equation
is compared with the one with dressed ladder. The elastic electromagnetic form
factors is calculated within the relativistic impulse approximation.Comment: 30 pages, 10 figures, accepted for publication in Phys. Rev.
Relativistic bound-state equations in three dimensions
Firstly, a systematic procedure is derived for obtaining three-dimensional
bound-state equations from four-dimensional ones. Unlike ``quasi-potential
approaches'' this procedure does not involve the use of delta-function
constraints on the relative four-momentum. In the absence of negative-energy
states, the kernels of the three-dimensional equations derived by this
technique may be represented as sums of time-ordered perturbation theory
diagrams. Consequently, such equations have two major advantages over
quasi-potential equations: they may easily be written down in any Lorentz
frame, and they include the meson-retardation effects present in the original
four-dimensional equation. Secondly, a simple four-dimensional equation with
the correct one-body limit is obtained by a reorganization of the generalized
ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving
three-dimensional equations is applied to this four-dimensional equation, thus
yielding a retarded interaction for use in the three-dimensional bound-state
equation of Wallace and Mandelzweig. The resulting three-dimensional equation
has the correct one-body limit and may be systematically improved upon. The
quality of the three-dimensional equation, and our general technique for
deriving such equations, is then tested by calculating bound-state properties
in a scalar field theory using six different bound-state equations. It is found
that equations obtained using the method espoused here approximate the wave
functions obtained from their parent four-dimensional equations significantly
better than the corresponding quasi-potential equations do.Comment: 28 pages, RevTeX, 6 figures attached as postscript files. Accepted
for publication in Phys. Rev. C. Minor changes from original version do not
affect argument or conclusion
Cost of porcine reproductive and respiratory syndrome virus at individual farm level – An economic disease model
Porcine reproductive and respiratory syndrome (PRRS) is reported to be among the diseases with the highest economic impact in modern pig production worldwide. Yet, the economic impact of the disease at farm level is not well understood as, especially in endemically infected pig herds, losses are often not obvious. It is therefore difficult for farmers and veterinarians to appraise whether control measures such as virus elimination or vaccination will be economically beneficial for their farm. Thus, aim of this study was to develop an epidemiological and economic model to determine the costs of PRRS for an individual pig farm. In a production model that simulates farm outputs, depending on farm type, farrowing rhythm or length of suckling period, an epidemiological model was integrated. In this, the impact of PRRS infection on health and productivity was estimated. Financial losses were calculated in a gross margin analysis and a partial budget analysis based on the changes in health and production parameters assumed for different PRRS disease severities. Data on the effects of endemic infection on reproductive performance, morbidity and mortality, daily weight gain, feed efficiency and treatment costs were obtained from literature and expert opinion. Nine different disease scenarios were calculated, in which a farrow-to-finish farm (1000 sows) was slightly, moderately or severely affected by PRRS, based on changes in health and production parameters, and either in breeding, in nursery and fattening or in all three stages together. Annual losses ranged from a median of € 75′724 (90% confidence interval (C.I.): € 78′885–€ 122′946), if the farm was slightly affected in nursery and fattening, to a median of € 650′090 (90% C.I. € 603′585–€ 698′379), if the farm was severely affected in all stages. Overall losses were slightly higher if breeding was affected than if nursery and fattening were affected. In a herd moderately affected in all stages, median losses in breeding were € 46′021 and € 422′387 in fattening, whereas costs were € 25′435 lower in nursery, compared with a PRRSV-negative farm. The model is a valuable decision-support tool for farmers and veterinarians if a farm is proven to be affected by PRRS (confirmed by laboratory diagnosis). The output can help to understand the need for interventions in case of significant impact on the profitability of their enterprise. The model can support veterinarians in their communication to farmers in cases where costly disease control measures are justified
Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
We use the worldline representation of field theory together with a
variational approximation to determine the lowest bound state in the scalar
Wick-Cutkosky model where two equal-mass constituents interact via the exchange
of mesons. Self-energy and vertex corrections are included approximately in a
consistent way as well as crossed diagrams. Only vacuum-polarization effects of
the heavy particles are neglected. In a path integral description of an
appropriate current-current correlator an effective, retarded action is
obtained by integrating out the meson field. As in the polaron problem we
employ a quadratic trial action with variational functions to describe
retardation and binding effects through multiple meson exchange.The variational
equations for these functions are derived, discussed qualitatively and solved
numerically. We compare our results with the ones from traditional approaches
based on the Bethe-Salpeter equation and find an enhanced binding contrary to
some claims in the literature. For weak coupling this is worked out
analytically and compared with results from effective field theories. However,
the well-known instability of the model, which usually is ignored, now appears
at smaller coupling constants than in the one-body case and even when
self-energy and vertex corrections are turned off. This induced instability is
investigated analytically and the width of the bound state above the critical
coupling is estimated.Comment: 62 pages, 7 figures, FBS style, published versio
Light-Front Bethe-Salpeter Equation
A three-dimensional reduction of the two-particle Bethe-Salpeter equation is
proposed. The proposed reduction is in the framework of light-front dynamics.
It yields auxiliary quantities for the transition matrix and the bound state.
The arising effective interaction can be perturbatively expanded according to
the number of particles exchanged at a given light-front time. An example
suggests that the convergence of the expansion is rapid. This result is
particular for light-front dynamics. The covariant results of the
Bethe-Salpeter equation can be recovered from the corresponding auxiliary
three-dimensional ones. The technical procedure is developed for a two-boson
case; the idea for an extension to fermions is given. The technical procedure
appears quite practicable, possibly allowing one to go beyond the ladder
approximation for the solution of the Bethe-Salpeter equation. The relation
between the three-dimensional light-front reduction of the field-theoretic
Bethe-Salpeter equation and a corresponding quantum-mechanical description is
discussed.Comment: 42 pages, 5 figure
Role of retardation in 3-D relativistic equations
Equal-time Green's function is used to derive a three-dimensional integral
equation from the Bethe-Salpeter equation. The resultant equation, in the
absence of anti-particles, is identical to the use of time-ordered diagrams,
and has been used within the framework of coupling to study the
role of energy dependence and non-locality when the two-body potential is the
sum of -exchange and crossed exchange. The results show that
non-locality and energy dependence make a substantial contribution to both the
on-shell and off-shell amplitudes.Comment: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev.
C56 (Nov. 97
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