Higher order Green functions in the theory of magnetism

1968 ◽  
Vol 28 (2) ◽  
pp. 73-74
Author(s):  
E. Becker
Keyword(s):  
Higher Order ◽  
Green Functions

COMPARISON OF THE ANOMALOUS AND NONANOMALOUS GENERALIZED SCHWINGER MODELS VIA THE FUNCTIONAL FORMALISM

1994 ◽  
Vol 09 (13) ◽  
pp. 2229-2244 ◽  
Author(s):  
ALVARO DE SOUZA DUTRA
Keyword(s):  
Correlation Functions ◽  
Lagrangian Density ◽  
Source Term ◽  
Higher Order ◽  
Green Functions ◽  
Functional Formalism ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Physical Consequences ◽  
Higher Order Lagrangian

We calculate the Green functions of the two versions of the generalized Schwinger model, the anomalous and the nonanomalous one, in their higher order Lagrangian density form. Furthermore, it is shown through a sequence of transformations that the bosonized Lagrangian density is equivalent to the former, at least for the bosonic correlation functions. The introduction of the sources from the beginning, leading to a gauge-invariant source term, is also considered. It is verified that the two models have the same correlation functions only if the gauge-invariant sector is taken into account. Finally, there is presented a generalization of the Wess-Zumino term, and its physical consequences are studied, in particular the appearance of gauge-dependent massive excitations.

scholarly journals New bounds for Shannon, Relative and Mandelbrot entropies via Hermite interpolating polynomial

2018 ◽  
Vol 51 (1) ◽  
pp. 112-130
Author(s):  
Nasir Mehmood ◽  
Saad Ihsan Butt ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Applied Sciences ◽  
Information Theory ◽  
Convex Function ◽  
Error Term ◽  
Probability Distributions ◽  
Jensen’S Inequality ◽  
Higher Order ◽  
Green Functions ◽  
Jensen's Inequality ◽  
Hermite Interpolating Polynomial

AbstractTo procure inequalities for divergences between probability distributions, Jensen’s inequality is the key to success. Shannon, Relative and Zipf-Mandelbrot entropies have many applications in many applied sciences, such as, in information theory, biology and economics, etc. We consider discrete and continuous cyclic refinements of Jensen’s inequality and extend them from convex function to higher order convex function by means of different new Green functions by employing Hermite interpolating polynomial whose error term is approximated by Peano’s kernal. As an application of our obtained results, we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.

scholarly journals Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients

2021 ◽  
Author(s):  
Hans-Christoph Grunau
Keyword(s):  
Principal Part ◽  
Present Note ◽  
Variable Coefficients ◽  
Higher Order ◽  
Elliptic Operators ◽  
Second Order ◽  
Dirichlet Boundary Conditions ◽  
Green Functions ◽  
Polyharmonic Operator ◽  
Bounded Smooth

AbstractEstimates from above and below by the same positive prototype function for suitably modified Green functions in bounded smooth domains under Dirichlet boundary conditions for elliptic operators L of higher order $$2m\ge 4$$ 2 m ≥ 4 have been shown so far only when the principal part of L is the polyharmonic operator $$(-\Delta )^m$$ ( - Δ ) m . In the present note, it is shown that such kind of result still holds when the Laplacian is replaced by any second order uniformly elliptic operator in divergence form with smooth variable coefficients. For general higher order elliptic operators, whose principal part cannot be written as a power of second order operators, it was recently proved that such kind of result becomes false in general.

HIGHER ORDER EQUATIONS AND CONSTITUENT FIELDS

1994 ◽  
Vol 09 (23) ◽  
pp. 4169-4183 ◽  
Author(s):  
D. G. BARCI ◽  
C. G. BOLLINI ◽  
L. E. OXMAN ◽  
M. ROCCA
Keyword(s):  
Simple Wave ◽  
Higher Order ◽  
Order Equation ◽  
Complex Conjugate ◽  
Green Functions ◽  
Fourth Degree ◽  
Causal Function ◽  
Complex Modes ◽  
Higher Order Equation ◽  
Conjugate Modes

We consider a simple wave equation of fourth degree in the D'Alembertian operator. It contains the main ingredients of a general Lorentz-invariant higher order equation, namely, a normal bradyonic sector, a tachyonic state and a pair of complex conjugate modes. The propagators are respectively the Feynman causal function and three Wheeler-Green functions (half-advanced and half-retarded). The latter are Lorentz-invariant and consistent with the elimination of tachyons and complex modes from free asymptotic states. We also verify the absence of absorptive parts from convolutions involving Wheeler propagators.

scholarly journals Integral representation of solutions to higher-order fractional Dirichlet problems on balls

2018 ◽  
Vol 20 (08) ◽  
pp. 1850002 ◽  
Author(s):  
Nicola Abatangelo ◽  
Sven Jarohs ◽  
Alberto Saldaña
Keyword(s):  
Integral Representation ◽  
Harmonic Functions ◽  
Boundary Data ◽  
Higher Order ◽  
Green Functions ◽  
Dirichlet Problems ◽  
Positive Power ◽  
Representation Of Solutions ◽  
Poisson Type

We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power [Formula: see text] of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders using explicit Poisson-type kernels and a new notion of higher-order boundary operator, which recovers normal derivatives if [Formula: see text]. Our results unify and generalize previous approaches in the study of polyharmonic operators and fractional Laplacians. As applications, we show a novel characterization of [Formula: see text]-harmonic functions in terms of Martin kernels, a higher-order fractional Hopf Lemma, and examples of positive and sign-changing Green functions.

scholarly journals Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group

2018 ◽  
Vol 97 (5) ◽  
Author(s):  
Yusuke Yoshimura ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Shinji Takeda ◽  
Ryo Sakai
Keyword(s):  
Renormalization Group ◽  
Higher Order ◽  
Green Functions ◽  
Order Tensor

scholarly journals Positivity of sums and integrals for n-convex functions via the Fink identity and new Green functions

2021 ◽  
Vol 66 (4) ◽  
pp. 613-627
Author(s):  
Asif R. Khan ◽  
◽  
Josip Pecaric ◽  
Keyword(s):  
Green Function ◽  
Convex Functions ◽  
Mean Value ◽  
Higher Order ◽  
Green Functions ◽  
Mean Value Theorems ◽  
The Green Function

We consider positivity of sum $\sum_{i=1}^np_if(x_i)$ involving convex functions of higher order. Analogous for integral $\int_a^bp(x)f(g(x))dx$ is also given. Representation of a function $f$ via the Fink identity and the Green function leads us to identities for which we obtain conditions for positivity of the mentioned sum and integral. We obtain bounds for integral remainders which occur in those identities as well as corresponding mean value theorems.

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