Further studies in aesthetic field theory VII

In this paper we discuss the clock paradox within the framework of the general theory of relativity. It is shown that in generalthe aging asymmetry exists. We also argue that the clock paradox, according to Mach's principle, is essentially a cosmological problem.     

Further studies in aesthetic field theory V; higher dimensions

We consider higher dimensional universes in which the universe is constructed from four-dimensional subuniverses. Independent parameters are introduced for the subuniverses. We then consider a small coupling between the subuniverses. Emphasis is placed on the eight-dimensional case. We find that the trends from the computer are in line with the natural boundary conditionsΓ _jk ⁱ →0 being satisfied. We do not find any significant improvement resulting as a consequence of the higher dimensions over and beyond the four-dimensional work we have done in previous papers.     

Further studies in aesthetic field theory VI: The lorentz group

In studying Γ _jk;l ⁱ = 0,g _ij;k = 0 field theory we require that the underlying structure (Γ _βγ ^α ,g _αβ ) be invariant underL (4), the four-dimensional Lorentz group. This can be accommodated into the theory by increasing the dimension to five. In our computer studies we still found a turnabout point forg ₄₄ on running down thex-axis, suggesting that this group may be consistent with a bounded particle. However, with still longer runs down thex-axis, there was some indication that a singularity may be developing.     

Further studies in aesthetic field theory; existence of a bounded particle

We have locked Into various possibilities within aesthetic field theory, particular attention to the case ofg=0. Theg=0 situation can be associated with the introduction of Newtonian absolute time into aesthetic field theory. If can be argued that Lorentz invariant boundary conditions for the universe are unlikely, giving impetus to the study ofg=0. We find that the field equations had to be modified from the form that they take wheng=0. Also, an infinite number of integrability equations have to be satisfied. We have required that our data have an underlying structure that Is invariant under O(3)×T. This set of date appeared satisfactory with respect to integrability and gave rise to a minimum ing _oo at the origin. After a long Computer run along the coordinate axes, we also found a bound on our particle-like object. This is the first time we have been able to obtain such a result.     

Further studies in aesthetic field theory. II: Equations fore αi

In a previous paper (Muraskin, 1973), we obtained a bounded particle in aesthetic field theory. The field equations there are implied by a set of equations for a system of basis vector variables,e _i . In this paper, we propose a simpler set of field equations fore _i . We find that a bounded particle solution to the equations still appears (as determined by axes runs). The particle appears basically similar to the particle found previously.     

Particle behavior in aesthetic field theory

We review the principles of aesthetic field theory and the latest results obtained from computer studies of the equations.     

Increased complexity in aesthetic field theory

We continue the program of looking for increased complexity within aesthetic field theory. We study a solution with five planar maxima and minima. Another solution in which we counted 19 planar maxima and minima is also studied. This latter solution was obtained by modifying our previous principles by allowing for an arbitrariness associated with the integration path in conjunction with the equation _jk:1 ⁱ =0.Supported by a research grant from the University of North Dakota.     

Particle behavior in aesthetic field theory

We discuss the structure of a particle system obtained in “aesthetic” field theory and study the evolution of this system in time. We find the particle system to have more structure than particles found by other authors investigating particlelike behavior in nonlinear field theories. Our particle system has a maximum center in proximity to a minimum center. Thus, we can interpret our system as being constructed of two bodies. We find that the maximum center and the minimum center move in straight lines, to computer accuracy. Thus, we have not found any nontrivial force laws. This suggests that the situation with respect to basic principles be kept fluid. So far as we know, we are the first investigators to study the trajectories of a two-body system which arises as a consequence of nonlinear field equations.     

New solutions in aesthetic field theory

We have obtained a large number of solutions to the aesthetic field equations. We discuss 19 solutions which appear to lead to bounded particle systems. One of the solutions is more complex (although only slightly) than the solution discussed in detail in Muraskin and Ring (1975). The solutions we have found have varied mathematical properties.     

A two-particle collision in aesthetic field theory

We have found a new computer solution to the aesthetic field equations. This solution describes a two-particle system with more structure than previously found. The contour lines show an arm structure. We have observed four arms around the maximum center. The location of the maximum (minimum) center is not along a straight line as a function of time. This is the first time that such an effect has been observed for any kind of nonlinear partial differential equation, so far as we know. A further discussion of the aesthetic principles leading to the field equations is given.     

Further studies in aesthetic field theory III: A bounded particle in Γ jk;l i =0,g ij;k =0 theory

In previous papers we showed that certain aesthetic ideas led to a bounded particle. In this paper, we show that a theory based on _jk;l ⁱ =0,g _ij;k =0 withg=0 can also lead to a bounded particle. This theory has the advantage that all tensors constructed fromg _ij , _jk ⁱ , _i are treated in a uniform way. Also, we have sixty-four distinct _jk ⁱ appearing. This was not the case in our previous work.     

A new particle solution in aesthetic field theory

In present theories a particle is commonly associated with a singularity of the field. A more realistic picture would describe the particle by an intense but singularity-free field. We have found a new solution to the aesthetic field equations for which the field associated with the particle has a very large magnitude. The particle appears to be bounded despite the large numbers appearing in the solution. We prove that this present solution is not equivalent to theO(3)-invariant solution discussed in Muraskin (1973b). Since our present solution appears well-behaved, the suggestion is that we do not confine ourselves toO(3)-invariant data in future work. Owing to the large magnitude fields, we were unable to study trajectories of the particle in any detail. There is nothing wrong, in itself, with large numbers. The present solution, which we have now studied, is the first instance in our work on aesthetic field theory in which large numbers appear without the suggestion of unboundedness.     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

Introduction of a second-rank antisymmetric tensor into null aesthetic field theory

We are able to incorporate an antisymmetric second-rank tensor into null aesthetic field theory. There are some changes in the solutions due to the introduction of this antisymmetric second-rank tensor, which we discuss. We are not able to find an acceptable bounded particle system in four space-time dimensions.     

Further studies on thickness vibrations of piezoelectric plate excited by parallel field

I.IntroductionThcthickncssvibrationsofahomogeneous-anisotropicpiezoclectriccrystalplatewithanexcitingficldparallcltothemajorsurfacesofthep1ate,andalsototheplanewavefront(calledasthepara11e1fic1dcxcitatloninbricO,havebccnana1yzedI'1.Theprimarybehaviourofthick-nessvibrationshasbecnobtaincdasthepIatewitharbitraryorientationisexcitedbythepara11elfield.Inthispapcr,wcwillgofurthcrtogivcancwformu1aofthemechanicalresonantfrequen-cyequation.ILqformisthesameasthercsonantequationofthepuremodeandiseasyt…     

平行场激励下压电板厚度振动的再探讨

本文进一步详细分析了平行场激励下压电板厚度振动,给出其诸振频率方程的新形式及耦合模的机电耦合系数,研究了耦合模及纯模的调频特性,并将结果用于两个实例中。     

A variational source method for numerical studies of field theory

A common method of measuring mass gaps in numerical studies of lattice field theories is to calculate the spatial dependence of the expectation value of test operators in the presence of a source. A novel source method is described which is variational: the mass extracted from expectation values measured at any separation is always an upper bound to the true mass. The method is illustrated with an example, the 0⁺⁺ glueball mass is computed in SU(3) lattice gauge theory at β = 5.7.     

Sinusoidal solutions to the aesthetic field equations

The aesthetic field equations do not resemble the wave equation, nor was the motivation behind them the wave equation. Nevertheless, we show that there exists a solution to the field equations that satisfies the wave equation. Integrability is also satisfied by this solution. Previously we showed that the Aesthetic Field Equations have particle solutions. Now we see that the equations also have sinusoidal solutions.     

Pseudo-Goldstino in field theory

We consider two SUSY-breaking hidden sectors which decouple when their respective couplings to the visible particles are switched off. In such a scenario one expects to find two light fermions: the Goldstino and the pseudo-Goldstino. While the former remains massless in the rigid limit, the latter becomes massive due to radiative effects which we analyze from several different points of view. This analysis is greatly facilitated by a version of the Goldberger-Treiman relation, which allows us to write a universal nonperturbative formula for the mass. We carry out the analysis in detail in the context of gauge mediation, where we find that the pseudo-Goldstino mass is at least around the GeV scale and can be easily at the electroweak range, even in low scale models. This leads to interesting and unconventional possibilities in collider physics and it also has potential applications in cosmology.