Session J10 - Particle Theory.
ORAL session, Sunday afternoon, April 29
Room 3, Renaissance Hotel

[J10.001] Nonperturbative solution of field theories quantized on the light cone

The numerical method of discrete light-cone quantization (DLCQ) and recent applications are described. Current work on supersymmetric Yang-Mills theories in 2+1 dimensions and on Pauli-Villars regularization in (3+1)-dimensional Yukawa theory is emphasized.

[J10.002] Frame-Independence of Exclusive Amplitudes in the Light-Front Quantization

While the particle-number-conserving convolution formalism established in the Drell-Yan-West reference frame is frequently used to compute exclusive amplitudes in the light-front quantization, this formalism is limited to only those frames where the light-front helicities are not changed and the good (plus) component of the current remains unmixed. For an explicit demonstration of such criteria, we present the relations between the current matrix elements in the two typical reference frames used for calculations of the exclusive amplitudes, i.e. the Drell-Yan-West and Breit frames and investigate both pseudoscalar and vector electromagnetic currents in detail. We find that the light-front helicities are unchanged and the good component of the current does not mix with the other components of the current under the transformation between these two frames. Thus, the pseudoscalar and vector form factors obtained by the diagonal convolution formalism in both frames must indeed be identical. However, such coincidence between the Drell-Yan-West and Breit frames does not hold in general. We give an explicit example in which the light- front helicities are changed and the plus component of the current is mixed with other components under the change of reference frame. In such a case, the relationship between the frames should be carefully analyzed before the established convolution formalism in the Drell-Yan-West frame is used.

[J10.003] Effective operators for heavy baryon systems in the combined heavy quark and large N_c limit

It has been shown recently [1,2] that it is very useful to consider the combined heavy quark and large N_c limit to describe the heavy baryons (baryons with a single heavy quark) and their excited states. An effective theory of the low-lying excited states of heavy baryons based on the combined expansion in powers of \lambda^1/2 (where \lambda \sim 1/m_Q, 1/N_c) has been developed [3]. In addition to the Hamiltonian a number of important heavy quark bilinears, e.g. an electroweak currents, can be expanded in powers of \lambda. The formalism for effective operators is similar to standard heavy quark effective theory. However, the pure heavy quark expansion diverges near the combined limit since residual momenta can be of order N_c. It will be shown in this talk how to reorganize the expansion, so that the new expansion contains no divergent terms. The effective expansion is used to calculate the semi-leptonic decay form factors.

[1] C.K.~Chow and T.D.~Cohen, Phys.~Rev.~Lett.~84 5474 (2000).

[2] C.K.~Chow and T.D.~Cohen, hep-ph/000313, Nucl.~Phys.~A to be published.

[3]C.K.~Chow, T.D.~Cohen and B.A.~Gelman, hep-ph/0012138.

[J10.004] Phenomenollogy of Heavy Baryons in the Combined Heavy Quark and Large N_c Limit

The dynamics of isoscalar heavy baryons containing a single heavy quark are described in the combined heavy quark and large N_c limit. In this combined limit, the expansion is in terms of \lambda ^1/2, where \lambda =\frac1m_Q,\frac1N_c. At next to leading order in \lambda ^1/2, there exists only two unknown parameters in the calculations of the spectroscopy, semi-leptonic decay form factors, and electromagnetic decays. Expressions for these quantities in terms of the unknown parameters are discussed, as are possible experimental tests.

[J10.005] Three-solitons scattering

The scattering angle for collisions between three solitons in the periodic O(3) sigma model is studied. The angle is found to be of sixty degrees, in accordance to theoretical predictions.

[J10.006] Nystrom plus Correction Method for Solving Bound State Equations in Momentum Space

A new method is presented for solving the momentum-space Schrodinger Equation with a linear potential. The Lande-subtracted momentum space equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the case of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved by calculating the numerical errors and adding the appropriate corrections. The end results are more accurate eigenvalues than those generated by the basis function method. The method is also shown to work for a relativistic equation such as the Thompson equation.

[J10.007] The Scattering Problem for the Square-Root Klein-Gordon Equation

The square-root Klein-Gordon equation, which employs a relativistic kinetic energy operator, is used extensively in phenomenological quark models as a way of incorporating relativity while maintaining an equation of the Schroedinger form. For quarkonium bound-state problems, the square-root operator is treated most conveniently in momentum space. However, the analysis of real decays of quarkonium states above flavor threshold requires some understanding of the behavior of the solutions in coordinate space. Unfortunately, the treatment in coordinate space is complicated by the nonlocal nature of the square-root operator. We will discuss these difficulties and present techniques for treating the scattering problem for this equation. Results for simple potentials will be presented and compared with nonrelativistic results.

[J10.008] Examples of Galilei-invariant mechanics

Concrete examples of Galilei-invariant mechanics are given using the 4-d formulation given by Havas [Rev. Mod. Phys. 36, 938 (1964)]. Using four-forces that are orthogonal to the four-velocity, Newtonian-like equations of motion are solved for cases involving one body in a force field and a special case of three interacting particles moving homographically in parallel planes. The usefulness of such cases for understanding interacting particles in Special Relativity is discussed.

[J10.009] NEW NEUTRAL CURRENT INTERACTION IN THE SU(2)XU(1) GAUGE GROUP, SPONTANEOUSLY BROKEN BY TWO HIGGS-KIBBLE DOUBLETS

We employ the n-dimensional coupling constant formalism to study the unification of interactions for the SU(2)XG gauge group. The neutral vector boson fields are defined in the n dimensional polar coupling constant system with the single "unifying" radial coupling constant and n-1 coupling angles. The formalism interrelates the neutral current charges,which define the neutral current interactions, and he electrically neutral generators. In this formalism the number of neutral charges and generators need not be the same. When G has just one generator, it can only be the weak hypercharge: G=U(1).So obtained SU(2)XU(1), however, is beyond the standard model as, in addition to the usual neutral current interactions, it contains the new neutral current interaction proportional to the hypercharge. It is mediated by the new neutral vector boson Zh . The coupling constant formalism, with two Higgs-Kibble doublets, generates vector boson mass spectrum. W and Z boson masses satisfy the usual relations while the Zh boson mass is calculated from first principle to be 43 GeV. As such,itis lighter than the Z boson. The effective coupling constant gh associated with the third neutral current interaction, is about 10 to 25e , the electromagnetic coupling constant.

[J10.010] Disproof of the Principle of Local Conservation of Energy in Classical Mechanics

The principle of local conservation of energy is critically examined for a continuous medium obeying the equation of local conservation of mass and Newton's 2nd law (i.e. Euler's equations). Although this principle is commonly assumed to be generally valid, it is shown that it is not valid even for such a simple medium when energy is properly distinguished from enthalpy. In other words, the principle of local conservation of energy cannot be simultaneously consistent with both the principle of local conservation of mass and Newton's 2nd law if consistently defined terminology is used.

[J10.011] A Model of Elementary Particle Interactions

There is a second kind of light which does not interact with our electrons. However it interacts with some of our protons (p) and some of our neutrons (n) which are both of two kinds (protons : p, p` ; neutrons : n`, n) differing in the two kinds of charges (Q1, Q2) associated with the two kinds of light. p[p`] and n`[n] have (Q1, Q2) values equal to (1,1) [(1,0)] and (0,0) [(0,1)] respectively. There is also a second kind of electron (Q2 = 1, Q1 = 0), equal in mass to our electron (Q1 = - 1, Q2 = 0), which does not interact with our kind of light. Three major scenarios S1, S2 and X4 arise. In S1, matter in the solar system on large scales is predominantly neutralized in both kinds of charges and the weak forces of attraction among the sun and planets are due to a fundamental force of nature. However in this scenario we must postulate that human consciousness is locked on to chemical reactions in the retina involving the first kind of light and the first kind of electrons only. It is oblivious to the simultaneous parallel chemical reactions governed by a chemistry which is based on the second kind of light and the second kind of anti-electrons and involves the same physical atoms manifesting different atomic numbers Z` ( = Q2). In scenario S2, matter in the solar system on large scales is predominantly neutralized in the first kind of charge only. In this scenario human consciousness is not restricted in its awareness to a narrowly circumscribed domain of physical reality………continued

[J10.012] Microcausality and Finslerian Quantum Fields

Microcausality is considered for a class of Finslerian quantum fields [1] in Minkowski spacetime by the calculation of the appropriate field commutators [2]. It is shown that, provided the adjoint field is consistently generalized, the necessary commutators are vanishing, and the field is microcausal. There are, however, Planck-scale modifications of the causal domain, but they only become significant for extremely large relative four-velocities at the separated spacetime points. The geometry of the causal domain indicates that near the Planck scale, causal connectivity of Finslerian quantum fields may occur between spacelike separated points, and also at larger scales for extremely large relative four-velocities [3]. For vanishing relative four-velocities, the causal domain is canonical. [1] H.E. Brandt, "Particle Geodesics and Spectra in the Spacetime Tangent Bundle," Reports Math. Phys., Vol. 45, 389 (2000). [2] H.E. Brandt, "Finslerian Quantum Fields and Microcausality," Found. Phys. Lett., Vol. 13, 307 (2000). [3] H. E. Brandt, "Causal Domain of Minkowski-Spacetime Tangent Bundle," to appear in Found. Phys. Lett. (2000).

[J10.013] On the Seeming Existence of Matter, and the Deeper Nature of Reality as Software Alone

This article presents an original and fundamental theory of quantum reality and reality in general. It posits that, deep down, the universe around us is in the nature of a logic tree, that we are parts of this tree, and that reality as we know it is an experience by us of some other parts of this tree. Under this theory, physics is looked upon as the experience of mathematical structures implicit in the parts of the above logic tree which correspond to our universe, the experience itself being dependent upon the nature of our consciousness (partly in the sense of Von Neumann and Eugene Wigner).

Because of the logic tree structure, the theory presented here may be called the software theory of reality. In this paper, this theory is elaborated and is compared and contrasted with current theories due to Bohr, Heisenberg, Wheeler, Bohm, Everett, Einstein, and Von Neumann.

[J10.014] World Matrix Self-Observability

The Copenhägen Interpretation of the Universe is conceived as a World Matrix which encodes ½-spin particles, gaugeons, higgons, gravity and the state vector. The organizing principle is a polynomial in the World Matrix which must be extremized after an *agendizing* technique which selects the coeffieients and method of encoding. An interesting feature of this theory is that the ½-spin particles may be boson (which we call *oxymorons*). One method of agendizing has some unusual predictions: ½-spin particles have 4 generations, the 4th of which consists of oxymorons *sans* neutrino, the other generations are normal except that the right-chiral neutrinos are oxymoronic therefore the neutrinos cannot have mass; there are 20 gauge bosons -- the electo-weak, 8 gluons and 8 rueons (which mix the flavors), 12 higgons which provide mass to the gaugeons and ½-spin particles, 2 rogue higgons which provide mass only to the higgons, and the graviton. This mix has zero vacuum energy. The project of agendizing to asure convergence has just begun.

Part J of program listing