Further studies in aesthetic field theory IV

We are able to obtain a bounded particle, with no indication of a singularity appearing, in several ways different from our previous papers. For one set of data we find slightly greater structure (more turnabout points) than previously. We discuss some of the properties of ten different sets of data.     

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 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.     

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. 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

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.     

Motion of a particle in a gravitational field in the special theory of relativity

The equations of motion for a particle moving in a gravitational field considered in planar spacetime are derived. A simplified form of these equations is obtained for the particular case of a centrosymmetric field subject to a simplifying assumption concerning the structure of the potential of a field with this sort of symmetry. Under this assumption the displacement of the perigee of the planets amounts to five-sixths of the value given by the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 48–52, March, 1977.     

On the existence of equilibrium states in local quantum field theory

It is shown that any local quantum field theory admits thermodynamical equilibrium states (KMS-states) for all positive temperatures provided it satisfies a nuclearity condition, proposed by Wichmann and one of the authors, which restricts the admissible number of local degrees of freedom.Dedicated to E. H. Wichmann on the occasion of his 60th birthday