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.     

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.     

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.     

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 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.     

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 stability in nonlinear scalar field theory

Using the direct Lyapunov method for distributed systems, the problem of stability of particlelike solutions of the equation of a scalar field with logarithmic nolinearity is solved. It is shown that nonlinearities of the Heaviside function type, which ensure the existence of exact regular solutions for the Klein-Gordon equation, are not a very fruitful approach because of the mathematical difficulties encountered in studying the stability of such solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–33, September, 1979.     

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.     

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.     

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.     

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 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 creation,classicality and related issues in quantum field theory: II. Examples from field theory

We adopt the general formalism, which was developed in Paper I to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum field theory in time dependent external backgrounds. In particular, we study the question of emergence of classicality in terms of the phase space evolution and its relation to particle production, and clarify some conceptual issues. We consider a quantized scalar field evolving in a constant electric field and in FRW spacetimes which illustrate the two extreme cases of late time adiabatic and highly non-adiabatic evolution. Using the time-dependent generalizations of various quantities like particle number density, effective Lagrangian etc. introduced in Paper I, we contrast the evolution in these two limits bringing out key differences between the Schwinger effect and evolution in the de Sitter background. Further, our examples suggest that the notion of classicality is multifaceted and any one single criterion may not have universal applicability. For example, the peaking of the phase space Wigner distribution on the classical trajectory alone does not imply transition to classical behavior. An analysis of the behavior of the classicality parameter, which was introduced in Paper I, leads to the conclusion that strong particle production is necessary for the quantum state to become highly correlated in phase space at late times.     

Asymptotic behavior of the Gell-Mann-Low function in quantum field theory

The reconstruction of the Gell-Mann-Low function in quantum field theory from its asymptotic series, whose first terms are calculated using perturbation theory, is discussed. This mathematical problem cannot be solved uniquely. Nevertheless, the desired function can be reconstructed in a certain finite range of coupling constant g under reasonable assumptions about this function. However, attemps to determine the behavior of the function for g→∞ are, in our opinion, groundless. Conditions under which the sum of the divergent perturbation series can rapidly decrease at infinity are determined.     

Evidence for almost point-like behavior of off-shell particles in field theory

Evidence is given in favor of the possibility that, in contrast to the rapid decrease of on-shell form factors, the off-shell form factors for both elementary and composite hadrons decrease as (q²)^?1 when the invariant momentum transfer q² becomes asymptotically large. Experimental implications are discussed.