Generaln-oder Cheracteristic Functionaland Its Variation Theory&General F(R) Gravity Theory And Research On Their Relative Applications

This dissertation reviews general n-order characteristic functional, Euler-Lagrangeequations and conservative quantities&general f(R) gravity and research on relativeeffects, and criticizes the some development processes of f(R) gravitational theory andPhantom&Quintessence Fields.This dissertation gives a general n-oder cheracteristic functional, uses quantitativecausal principle to derive the general variational principle, further deducesEuler-Lagrange equation and conservative quantities for general n-oder cheracteristicfunctional, and reveals the link between the quantitative causal principle and therelativity principle, derives general Newton’s first, second and third laws, but the thirdlaws is also a new law, it is the theorem that force is zero in translational invariance,and reveal its general physical meaning of classic mechanics. And the achieved resultshave been successful applied to the galaxy gravitational potential correction, molecularpotential, quark confinement potential, etc., and the results are consistent with thephysical experiments.This dissertation, in terms of quantitative causal principle, deduces relativityprinciple, gives unified descriptions of quantitative causal principle, relativity principleand Euler-Lagrange equations. This dissertation further gets that the correspondingacceleration field can be replaced by the gravitational field strength, and shows thatabsolute acceleration, drawing acceleration and relative acceleration are, respectively,equivalent to corresponding absolute gravitational field strength, drawing gravitationalfield strength and relative gravitational field strength. Therefore, we have deduced akind of new physical effects, i.e., under the condition of existing acceleration, in therelative reference system, the measured relative strength of the gravitational fieldincreases or decreases with change of the drawing acceleration system. And thisdissertation achieves another new physical effect, i.e., in relative reference systemunder acceleration condition, the measured electric field strength has increasing anddecreasing effects. And this dissertation gives an important application to measureelectric field strength in relative reference spaceship.This dissertation generally gives a new general action of f(R) gravity and Phantom&Quintessence fields of coupling to scalar curvature, deduces Euler-LagrangeEquations of different fields, and gives matter tensor and effective matter tensor. Thusthis dissertation achieves the general pressure, density and speed sound of the newgeneral field action, investigates cosmological different evolutions with inflation.Furthermore, this dissertation investigates a general f(R) gravity theory with a generalmatter action, obtains the field different equations, general matter tensor and effective matter tensor, further achieves effective Strong Energy Condition (SEC) and effectiveNull Energy Condition (NEC), and proves that when f(R) approaches to R, the effectiveSEC and the effective NEC approach, respectively, to the usual SEC and the usualNEC. Finally, this dissertation further gives a general action of f(R) gravity and manyQuintessence&Phantom fields and very more applications can be done.This dissertation gives not only f(R) gravity reduction, for the first time, but also akind of new method processing and solving equations, overcomes non-consistent andnon-symmetric problems in quantization effects of non-linear f(R) and linear matterLagrangianLm, discovers nonlinear general f(R) identity, deduces Euler-LagrangeEquations of general matter Lagrangian function b(Lm) coupling with generally curvedspacetime, achieves new general conformal structure symmetric equations ofinteractions of general f(R) gravity and general matter Lagrangian function b(Lm), andwe do application of this dissertation’s theory to cosmology. We discover thatEinstein’s equation should be rewritten as the same tensor structure equation thatmathematical tensor structures of two sides of Einstein’s equation are the same, i.e.,structure symmetric equation, and we generalize the theory to a general interactionsystem of general matter Lagrangian function b(Lm) and a general function f(R) ofarbitrary high order scalar curvature R. And this dissertation gives the new generalconformal structure symmetric theory simplifying differently modified f(R) gravities.