scholarly journals On the cosmological solutions in Weyl geometry

2021 ◽  
Vol 2021 (11) ◽  
pp. 053
Author(s):  
V.A. Berezin ◽  
V.I. Dokuchaev ◽  
Yu. N. Eroshenko ◽  
A.L. Smirnov
Keyword(s):  
Equations Of Motion ◽  
Consistency Condition ◽  
Conformal Factor ◽  
Cosmological Term ◽  
The Self ◽  
Curvature Scalar ◽  
Weyl Geometry ◽  
Cosmological Solutions ◽  
Complete Set ◽  
Self Consistency

Abstract We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.

scholarly journals NNLO classical solution for Lipatov’s effective action for reggeized gluons

2019 ◽  
Vol 34 (20) ◽  
pp. 1950111
Author(s):  
S. Bondarenko ◽  
S. Pozdnyakov
Keyword(s):  
Effective Action ◽  
Equations Of Motion ◽  
The Self ◽  
Classical Solutions ◽  
Transversality Conditions ◽  
Loop Contribution ◽  
Recursive Scheme ◽  
Fermion Loop ◽  
The One ◽  
Self Consistency

We consider the formalism of small-[Formula: see text] effective action for reggeized gluons[Formula: see text] and, following the approach developed in Refs. 11–17, calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated that for each perturbative order, the self-consistency of the equations of motion is equivalent to the transversality conditions applied to the solution of the equations, these conditions allow to construct the general recursive scheme for the solution’s calculation. The one fermion loop contribution to the classical solutions and application of the obtained results are also discussed.

THE SELF-CONSISTENT MATHIEU PROBLEM

1964 ◽  
Vol 42 (2) ◽  
pp. 329-348
Author(s):  
J. Vail
Keyword(s):  
Fermi Surface ◽  
Energy Gap ◽  
Mass Density ◽  
Mathematical Problem ◽  
Consistency Condition ◽  
The Self ◽  
Particle Spectrum ◽  
Self Consistent ◽  
The One ◽  
Self Consistency

The one-dimensional many-fermion system with weak attractive interaction, which is known to have self-consistent Hartree solutions corresponding to either uniform or spatially periodic mass density, is discussed as a physical model and as a mathematical problem. The Hartree problem for sinusoidal mass density leads to the self-consistent Mathieu problem, which is analyzed for the case where the first Brillouin zone boundary does not necessarily coincide with the Fermi surface (no energy gap between ground and single-particle excited states). The Mathieu equation is solved in the weak-binding approximation in the vicinity of the two lowest band gaps, the self-consistency condition is analyzed in detail, and the N-particle energy is calculated for various cases. The results suggest that the periodic state will not have lower energy than the uniform state unless the first gap in the one-particle spectrum lies near the Fermi surface. The fact that self-consistency can be obtained for a considerable range of periodicities suggests that the periodic solutions may be of importance in some many-fermion systems.

Zur Theorie der Supraleitung in planparallelen Schichten geringer Dicke

1967 ◽  
Vol 22 (7) ◽  
pp. 985-997 ◽  
Author(s):  
Henning Raufuss
Keyword(s):  
Film Thickness ◽  
Consistency Condition ◽  
Quantitative Comparison ◽  
Gap Function ◽  
The Self ◽  
Energy Integral ◽  
Critical Temperatures ◽  
Planar Films ◽  
Basic Equations ◽  
Self Consistency

The GORKOV equations are solved for ideal planar films of superconductors. For the purpose of comparison, two different formulations of the self-consistency condition are used; the first is characterised by a cut-off factor in the energy integral, the second by the termination of the ω summation at the same cut-off value. Certain values of the film thickness (those corresponding to resonance intervalls in the sense of THOMPSON and BLATT) are excluded, but they are not decisive to this treatment. By this means, a fairly accurate check of the error in the approximation is made possible. This allows a quantitative comparison of the critical temperatures and of the two forms of the gap function calculated from the two formulations of the basic equations.At absolute zero, both formulations of the theory become equivalent and lead to essentially identical relations between the gap function and film thickness. However, the critical temperature which results from the termination of the ω summation is noticeably higher than that calculated with the help of the energy cut-off.

Comparison of the major force constant models for cubic systems using a self-consistency condition

1979 ◽  
Vol 57 (12) ◽  
pp. 2053-2065 ◽  
Author(s):  
R. A. Moore ◽  
J. C. Upadhyaya
Keyword(s):  
Force Constant ◽  
Consistency Condition ◽  
Pair Potential ◽  
Tensor Force ◽  
The Self ◽  
Nearest Neighbour ◽  
Axially Symmetric ◽  
Phonon Spectra ◽  
Cauchy Relation ◽  
Self Consistency

Previously noted similarities between the central pair potential, CPP, the DeLaunay angular force, DAF, and the Lehman, Wolfram, and De Wames axially symmetric, AS, models for lattice dynamics coupled with criticisms of the DAF model, not applicable to the CPP model, has resulted in a puzzling and confusing picture. New physical arguments are used to develop a self-consistency condition, essentially unrecognized previously, which must be included in the use of all these force constant models. In this event, all of the above three models are proven to be identical. We then go on to examine the Clark–Gazis–Wallis, CGW, model. A systematic procedure is presented allowing a practical extension of the expression for the force constants from the current first and second nearest neighbour interactions to include third nearest neighbour interactions. For fcc systems we show that the previous expressions are incomplete and, consequently, overly restrictive and misleading and, hence, causing a current controversy. Also, we point out that the CGW model reproduces the general tensor force, GTF, model, at least to third nearest neighbour interactions. It is important to note that the application of the above mentioned self-consistency condition restores the Cauchy relation in all the models. Finally, numerical results are presented for the phonon spectra of the bcc metals Na and Nb and the fcc metals Cu and Au in order to demonstrate the practical effect of the self-consistency condition. This effect is seen to be larger for metals having larger Cauchy discrepancies. It is inferred that the force constant models, and hence the self-consistency condition, must be modified to yield the Cauchy discrepancy.

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