Physics Commons^™

An Extension Of The Rishon Model, Paul Finkler

Paul Finkler Papers

We present an extension of the Rishon Model of Harari, et. al. [1] [2] [3] In that model, the first generation leptons and quarks are each made from three rishons of two varieties, T and V as follows: v_e = V V V , e⁺ = T T T , d = T V V , and u = T T V . In addition to the original rishons and their anti-rishons T and V , we introduce the dark rishon X and its anti-rishon X; all have spin 1/2.

An exciting possibility that emerges from this idea …

Relativistic Momentum, Paul Finkler

Paul Finkler Papers

Introductory treatments of relativistic dynamics rely on the invariance of momentum conservation (i.e., on the assumption that momentum is conserved in all inertial frames if it is conserved in one) to establish the relationship for the momentum of a particle in terms of its mass and velocity. By contrast, more advanced treatments rely on the transformation properties of the four-velocity and/or proper time to obtain the same result and then show that momentum conservation is invariant. Here, we will outline a derivation of that relationship that, in the spirit of the more advanced treatments, relies on an elemental feature of …

Numerical Study Of A High-Order Quasiconserved Quantity In The Henon-Heiles Problem, Paul Finkler, C. Edward Jones, Glenn A. Sowell

Paul Finkler Papers

Recent efforts to derive and study a quasiconserved quantity K in the Henon-Heiles problem in terms of a single set of variables are discussed. Numerical results are given, showing how the value of such a quantity varies with time and order in a power-series expansion for K in terms of monomials of the coordinates and velocities. The lowest order in the power series for K corresponds to n =4 and the highest order to n =27, so that 24 orders are included in the series. The results are compared with an earlier study by the authors [Phys. Rev. A 42, …

Construction Of A Quasiconserved Quantity In The Henon-Heiles Problem Using A Single Set Of Variables, Paul Finkler, C. Edward Jones, Glenn A. Sowell

Paul Finkler Papers

The problem of finding the coefficients of a simple series expansion for a quasiconserved quantity K for the Henon-Heiles Hamiltonian H using a single set of variables is solved. In the past, this type of approach has been problematic because the solution to the equations determining the coefficients in the expansion is not unique. As a result, the existence of a consistent expression for K to all orders had not previously been established. We show how to deal with this arbitrariness in the expansion coefficients for K in a consistent way. Due to this arbitrariness, we find a class of …

Possible Conserved Quantity For The Henon-Heiles Problem, Paul Finkler, C. Edward Jones, Glenn A. Sowell

Paul Finkler Papers

We study a power-series expansion for a conserved quantity K in the case of the two-dimensional Henon-Heiles potential. An alternative technique to that of Gustavson [Astron. J. 71, 670 (1966)] is applied to find the coefficients in the expansion for K. The technique is used to determine twelve orders for the conserved quantity K, more than twice as many as that calculated by Gustavson. We investigate the degree of constancy of our truncated K in regions where the motion is known to be chaotic and also where it is nonchaotic.

Self-Consistent Phases In Topological Particle Theory, Paul Finkler, C. Edward Jones

Paul Finkler Papers

To be a self-contained theory, topological particle theory should explain from the basis of its own stated framework of assumptions (nonlinear self-consistency equations, pole factorization, crossing symmetry, and Hermitian analyticity} all the mathematical properties and numerical values of scattering amplitudes. This paper attempts to move the theory in this direction by showing that the phases of the zero-entropy amplitudes in the theory are, in fact, determined by the above framework of assumptions except for trivial ambiguities that appear to have no physical consequences. This extends previous work on this subject and removes the need for certain extra assumptions. Once the …

Derivation Of Discrete Invariances (T, C, And P) And The Connection Between Spin And Statistics In Topological Particle Theory, C. E. Jones, Paul Finkler

Paul Finkler Papers

For purely hadronic processes, the standard connection between spin and statistics as well as separate invariances under charge conjugation, parity, and time reversal are shown to be consequences of self-consistency in topological particle theory.

Bilinear Equation For The Cylinder With Overlap And The Pomeron Residue, Paul Finkler, C. Edward Jones

Paul Finkler Papers

A bilinear integral equation for the cylinder is derived within the meson sector of the theory of dual topological unitarization. The equation is more general than conventional linear cylinder equations since it includes regions of phase space in which produced particles overlap in rapidity. The equation also permits a simple treatment of phase space which corresponds to that of the planar bootstrap problem. Two classes of solutions are found, only one of which results in the Pomero'n-f identity. This treatment also indicates that the residue of the Pomeron may be twice as large as that suggested by earlier calculations …

Path-Integral Formulation Of Scattering Theory, Paul Finkler, C. Edward Jones, M. Misheloff

Paul Finkler Papers

A new formulation of nonrelativistic scattering theory is developed which expresses the S matrix as a path integral. This formulation appears to have at least two advantages: (1) A closed formula is obtained for the S matrix in terms of the potential, not involving a series expansion; (2) the energy-conserving δ function can be explicitly extracted using a technique analogous to that of Faddeev and Popov, thereby yielding a closed pathintegral expression for the T matrix. The introduction of the concept of the classical interaction picture provides considerable physical insight into this formulation. This formulation also suggests a successionof improvements …

Path Integrals With Arbitrary Generators And The Eigenfunction Problem, William B. Campbell, Paul Finkler, C. E. Jones, M. N. Misheloff

Paul Finkler Papers

We generalize the path integral formalism of quantum mechanics to include the use of arbitrary infinitesimal generators, thus providing explicit expressions for solutions of a wide class of differential equations. In particular, we develop a method of calculating the eigenfunctions of a large class of operators.

Deduction Of Asymptotic Steinmann Relations From The Regge Hypothesis, Paul Finkler, C. Edward Jones, M. Misheloff

Paul Finkler Papers

The analytic structure of the double-Regge vertex, which has previously been obtained from the Steinmann relation, is derived by using a natural generalization of the Regge hypothesis.

Limited Resurrection Of The Born Approximation, Paul Finkler

Paul Finkler Papers

It is shown that the ordinary Born approximation for pn and pp̅ charge-exchange scattering correctly accounts for (1) the shape of the forward peak for 0 ≤ (-t) ≤ µ²/2 at P_L = 8 GeV/c, and (2) the energy dependence of the cross sections at t=0 in the energy range P_L,=2—8 GeV/c. This result is analogous to the well-known success of the electric Born approximation in Π⁺ photoproduction. It is then shown that the simplest interpretation of this surprising result within the framework of Regge-pole theory is in terms …

Existence Of Fixed Poles And Their Role In Conspiracy, Paul Finkler

Paul Finkler Papers

It is shown that unitarity allows fixed poles at certain nonsense points of either right or wrong signature. The conditions for the existence of these poles are found. These conditions are then used to locate the poles allowed in hadronic reactions. Possible mechanisms for the poles are considered. It is then argued that fixed poles provide the most natural explanation of the conspiracy phenomenon.

On The Relation Between Hard-Core And Velocity-Dependent Potentials: An Application To The Photonuclear Sum Rules, Paul Finkler, H. S. Valk

Paul Finkler Papers

A canonical transformation relating hard-core and velocity-dependent nucleonnucleon potentials is applied to the Srivastava potential and an equivalent hard-core potential is found. It is shown that the deuteron photonuclear electric-dipole integrated and bremsstrahlung-weighted cross sections resulting from the two equivalent potentials are essentially the same. The reasons for this agreement suggest that differences between the two sets of cross sections may remain small in other nuclei employing this type of potential.

Evaluation Of The Dispersion Relations Of Photoproduction, Paul Finkler

Paul Finkler Papers

A modification of the Omnes method is used to solve the singular integral equations for the 3-3 partialwave amplitudes of photoproduction. The effects of multipion production are assumed to be negligible. The method requires a knowledge of the phase at all energies. Consequently, it is necessary to treat the corresponding pion-nucleon scattering problem to determine the eBect of the high-energy behavior of the phase on the solution for the scattering amplitude at low energies. The sharply resonant nature of the problen suggests an approximation in the form of solution, rather than in the Born terms, which leads to relatively simple …