120403374
THREE-TRIPLET MODEL WITH DOUBLE SU(3) SYMMETRY
122263475
Three triplets, paraquarks, and ''colored'' quarks
121149545
Generalization and Interpretation of Dirac's Positive-Energy Relativistic Wave Equation
We generalize Dirac's new equation so as to deacribe particles of mass m and arbitrary spin s. The same remarkable properties are found: positive energy, non-negative density, a conserved four-vector current, and the impossibility of minimal electromagnetic interaction. We show that the particles described by a subset of these equations are composites of two subparticles interacting by a relativistic action-at-a-distance interaction charactcrized by two harmonic oscillators. For these composite particles we find a linear relation between the square of the mass and the spin. We emphasizr that the essential content of the generalized new Dirac equation is that it constitutes an example of a convariant solution for two interacting particles, and provides an explicit examaple of a new quantal subdynamics distinct from the (classical) front relativistic dynamics of Dirac. (auth)
11115006
Environmental adaptability and mutants: Exploring new concepts in particle transport for multi-scale simulation
Ongoing investigations to introduce software techniques suitable to support new experimental requirements for multi-scale simulation are discussed.
123307684
Hadronic regge sequences as primitive realizations of SL(3,R) symmetry☆
Abstract Four primitive infinite dimensional unitary representations of the group of rotations and deformations - SL(3,R) - are constructed and associated with the four Regge trajectories: π, ϱ, N, Δ. The model predicts E2 transition moments and a power law for E versus j consistent with the Chew-Frautschi relation E∼j 1 2 .
119908252
George Sudarshan, No-Go theorems and the exclusion principle
We review two areas of my work that were directly and indirectly initiated and inspired by George. One is the proofs of no-go theorems in combining the spacetime and internal symmetries in non-trivial ways and the other is how Georges firm conviction on the fundamentality of the spin-statistics theorem helped to expand the domain of applicability of the spin-statistics theorem into the arena of quarks and gluons, going far beyond the original application of the exclusion principle in atomic physics. In order to provide deeper understanding of mass differences of particles belonging to spin-degenerate multiplets, attempts have been made to see if some non-trivial way of embedding the Lorentz group and internal symmetry groups such as SU(2) and SU(3) into a larger group. When a hint of no-go theorem (that such non-trivial embedding cannot be achieved) first appeared, George went to work and led many of us, including myself, into this area of research. A series of proofs of no-go theorems by George, myself and others eventually led to the definitive proof by Lochlainn O'Raifeartaigh that came to be known as the ORaifeartaigh theorem. Lochlainn also joined George at Syracuse at the same time I went there. The second area in which George had significant influence on my work is his fervent belief in the fundamental importance of the spin-statistics relationship. First postulated by Worlfgang Pauli to explain the periodic table of elements, the relationship the exclusion principle has exceeded far beyond its original domain of validity. The relationship has been upheld across the scale molecular, atomic, and nuclear structures. What is less known is the fact the relationship continues to remain valid in scales smaller than nucleons. The spin-statistics relationship was one of the compelling reasons for Nambu and I to introduce a new set of then undiscovered degrees freedom for quarks inside nucleons. This new degrees of freedom came to be called the color charges of quarks and it led to the non-Abelian gauge field theory of the strong interactions known today as the quantum chromodynamics. Georges insight into the spin-statistics relationship was indispensable in the birth of the new theory of the strong force.
119174283
Asymptotics of spinfoam amplitude on simplicial manifold: Lorentzian theory
This paper studies the large-j asymptotics of the Lorentzian Engle–Pereira–Rovelli–Livine (EPRL) spinfoam amplitude on a 4D simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three types of regions and , where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted to implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted to is degenerate of type-A in our definition of degeneracy, but it implies a nondegenerate discrete Euclidean geometry in , (3) the critical configuration restricted to is degenerate of type-B, and it implies a vector geometry in . With the critical configuration, we further make a subdivision of the regions and into sub-complexes (with boundaries) according to their Lorentzian/Euclidean oriented 4-volume V4(v) of the 4-simplices, such that sgn(V4(v)) is a constant sign on each sub-complex. Then in each sub-complex or , the spinfoam amplitude at the critical configuration gives the Regge action in a Lorentzian signature or an Euclidean signature respectively. The Regge action reproduced here contains a sign prefactor sgn(V4(v)) related to the oriented 4-volume of the 4-simplices. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with an on-shell connection. Finally, the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated with different types of geometries.
6895472
Generating entangled photons from the vacuum by accelerated measurements: Quantum-information theory and the Unruh-Davies effect
quantum communications between accelerated and stationary observers. We find that the projective measurement by a uniformly accelerated observer can excite real particles from the vacuum in the inertial frame, even if no additional particles are created by the measurement process in the accelerating frame. Furthermore, we show that the particles created by this accelerating measurement can be highly entangled in the inertial frame, and it is also possible to use this process to generate even maximally entangled two-qubit states by a certain arrangement of measurements. As a by-product of our analysis, we also show that a single qubit of information can be perfectly transmitted from the accelerating observer to the inertial one. In principle, such an effect could be exploited in designing an entangled-state generator for quantum communication.
16629504
Five-dimensional Brans-Dicke theory and cosmic acceleration
We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to five dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the underlying 5-dimensional spacetime, the theory is reduced to a 4-dimensional theory where the 4-metric is coupled with two scalar fields. The cosmological implication of this reduced theory is then studied in the Robertson-Walker model. It turns out that the two scalar fields may account naturally for the present accelerated expansion of our universe. The observational restriction of the reduced cosmological model is also analyzed.
118178605
SL(2,C) Chern–Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: Semiclassical geometry
Abstract We study the expectation value of a nonplanar Wilson graph operator in SL ( 2 , C ) Chern–Simons theory on S 3 . In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F 2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL ( 2 , C ) Chern–Simons theory in 3 dimensions with knotted graph defects.
119275326
4-dimensional spin-foam model with quantum Lorentz group
We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infra-red divergence, thus gives a finite partition function on a fixed triangulation. We expect this quantum group spin-foam model is a spin-foam quantization of discrete gravity with a cosmological constant.