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.
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 .
122263475
Three triplets, paraquarks, and ''colored'' quarks
120561444
Comment on the paper entitled «On the Poincaré noninvariance of a recent alternative to the Dirac equation»
122507140
Diquark color excitation and the narrow resonances
The new narrow resonances are interpreted in the three-triplet model with integral baryon numbers as diquark color excitations of the qq +- q-barq-bar type. Hadronic decays, ..gamma.. transitions, and coupling to ..gamma.. occur through impurity qq-bar admixtures. Except for the coupling to ..gamma.., all decay rates are suppressed. The enhancements above 4 GeV in hadronic cross sections are attributed to qq-bar color octets or still higher diquark levels. (AIP)
121619492
A possible mechanism for CP nonconservation
119144559
Cosmological Constant in LQG Vertex Amplitude
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity) embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.
118376309
Spin-foam fermions: PCT symmetry, Dirac determinant and correlation functions
We discuss fermion coupling in the framework of spin-foam quantum gravity. We analyze the gravity-fermion spin-foam model and its fermion correlation functions. We show that there is a spin-foam analogue of PCT symmetry for the fermion fields on a spin-foam model, which is proved for spin-foam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spin-foams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.
118610209
A path integral for the master constraint of loop quantum gravity
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator. By the standard technique of skeletonization and the coherent state path integral, we derive a path-integral formula from the group averaging for the master constraint operator. Our derivation in this paper suggests there exists a direct link connecting the canonical loop quantum gravity with a path-integral quantization or a spin-foam model of general relativity.
119699042
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of . The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation.
14607839
Exhaustive ghost solutions to Einstein-Weyl equations for two dimensional spacetimes
Exhaustive ghost solutions to Einstein-Weyl equations for two dimensional spacetimes are obtained, where the ghost neutrinos propagate in the background spacetime, but do not influence the background spacetime due to the vanishing stress-energy-momentum tensor for the ghost neutrinos. Especially, those non-trivial ghost solutions provide a counterexample to the traditional claim that the Einstein-Hilbert action has no meaningful two dimensional analogue.