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 A Liouville theorem for the higher-order fractional Laplacian

2019 ◽  
Vol 21 (02) ◽  
pp. 1850005 ◽  
Author(s):  
Ran Zhuo ◽  
Yan Li
Keyword(s):  
Positive Solutions ◽  
Fractional Laplacian ◽  
Liouville Theorem ◽  
Integral Form ◽  
Higher Order ◽  
Order Equation ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Higher Order Equation ◽  
Fractional Equation

We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space [Formula: see text] by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on [Formula: see text] through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.

On the Decomposition of Spinor Fields which satisfy a Nonlinear Higher Order Equation

1983 ◽  
Vol 38 (12) ◽  
pp. 1293-1295
Author(s):  
D. Großer
Keyword(s):  
Field Theory ◽  
Higher Order ◽  
Order Equation ◽  
Field Theories ◽  
First Order ◽  
Spinor Fields ◽  
Fermion Fields ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Higher Order Equation

Abstract A field theory which is based entirely on fermion fields is non-renormalizable if the kinetic energy contains only derivatives of first order and therefore higher derivatives have to be included. Such field theories may be useful for describing preons and their interaction. In this note we show that a spinor field which satisfies a higher order field equation with an arbitrary nonlinear selfinteraction can be written as a sum of fields which satisfy first order equations.

UNITARITY AND COMPLEX MASS FIELDS

1993 ◽  
Vol 08 (18) ◽  
pp. 3185-3198 ◽  
Author(s):  
C. G. BOLLINI ◽  
L. E. OXMAN
Keyword(s):  
Absorptive Part ◽  
Vacuum Expectation ◽  
Complex Conjugate ◽  
Expectation Values ◽  
Self Energy ◽  
Causal Function ◽  
S Matrix ◽  
Complex Mass ◽  
Real Mass ◽  
Higher Order Equation

We consider a field obeying a simple higher order equation with a real mass and two complex conjugate mass parameters. The evaluation of vacuum expectation values leads to the propagators, which are (resp.) a Feynman causal function and two complex conjugate Wheeler–Green functions (half retarded plus half advanced). By means of the computation of convolutions, we are able to show that the total self-energy has an absorptive part which is only due to the real mass. In this way it is shown that this diagram is compatible with unitarity and the elimination of free complex-mass asymptotic states from the set of external legs of the S-matrix. It is also shown that the complex masses act as regulators of ultraviolet divergences.

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