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.
17797254
HAMILTONIAN ANALYSIS OF n-DIMENSIONAL PALATINI GRAVITY WITH MATTER
We consider the Palatini formalism of gravity with cosmological constant Λ coupled to a scalar field ϕ in n dimensions. The n-dimensional Einstein equations with Λ can be derived by the variation of the coupled Palatini action provided n>2. The Hamiltonian analysis of the coupled action is carried out by a 1+(n-1) decomposition of the spacetime. It turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of Λ and ϕ while the n-dimensional Palatini action could not give a dynamical formalism of connection directly.
119628044
On the Asymptotics of Quantum Group Spinfoam Model
Recently a quantum group deformation of EPRL spinfoam model was proposed in arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and Meusburger. It is interesting to study the high spin asymptotics of the quantum group spinfoam model, to see if it gives the discrete Einstein gravity with cosmological constant as its semiclassical limit. In this article we propose a new technique, which can simplify the analysis of the high spin asymptotics for quantum group spinfoam vertex amplitude. This technique can generalize the spinfoam asymptotic analysis developed by Barrett, et al to quantum group spinfoam. As a preparation of asymptotic analysis, we define and analyze the coherent states and coherent intertwiners for quantum group, which has certain "factorization properties". We show that in the high spin limit of quantum group spinfoam, many q-deformed noncommutative ingredients become classical and commutative. In particular, the squared norm of coherent intertwiner and the (Euclidean) vertex amplitude become integrals on classical group, while there are some additional terms (written in terms of classical group variables) make quantum group corrections to the usual (classical group) coherent intertwiner and vertex amplitude. These quantum group correction terms turn out to be proportional to the deformation parameter, which hopefully gives the cosmological term as its semiclassical limit.
5145645
Quantum dyanmics of loop quantum gravity
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturbative quantum theory for the Lorentzian gravitational field on a four-dimensional manifold. In this approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of "quantum Riemannian geometry", which is discrete at a fundamental scale. In the investigation of quantum dynamics, the classical expressions of constraints are quantized as operators. The quantum evolution is contained in the solutions of the quantum constraint equations. On the other hand, the semi-classical analysis has to be carried out in order to test the semiclassical limit of the quantum dynamics. 
In this thesis, the structure of the dynamical theory in loop quantum gravity is presented pedagogically. The outline is as follows: first we review the classical formalism of general relativity as a dynamical theory of connections. Then the kinematical Ashtekar-Isham-Lewandowski representation is introduced as a foundation of loop quantum gravity. We discuss the construction of a Hamiltonian constraint operator and the master constraint programme, for both the cases of pure gravity and matter field coupling. Finally, some strategies are discussed concerning testing the semiclassical limit of the quantum dynamics.
118608710
Spinfoam fermions
A serious shortcoming of spinfoam loop gravity is the absence of matter. See for instance [1, 2] and full references therein. Here we study a minimal coupling of the theory with a chiral fermion field and a Yang-Mills field. We find that the dynamical coupling of a fermion to quantum gravity is surprisingly simple in the spinfoam formalism. This result resonate with similar ones in early canonical loop theory [3, 4]: the naive fermion hamiltonian was found to be just the extension of the simple “shift” form [5] of the gravitational hamiltonian, to the open ends of the gravitational Faraday lines, which represent fermions. Here we find that in the spinfoams context the fermion dynamics is a natural extension of the gravitational amplitude to spin-networks with spin1 2 open-ends at the nodes. In the presence of fermions, it is then easy to add YangMills fields by promoting a global symmetry to a local symmetry. The dynamics can then be generated à la Zeld’hovic [6, 7] from fermion loops. For earlier studies on how to couple fermions to a discretized gravitational field, see [8–11]. For detailed studies of fermions in the loop quantum gravity canonical formalism, see [12–15]. On fermions in 3d, spinfoams and quantum cosmology and the effect of fermions on Holst gravity, see also [16–20].
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.
119951520
On a difficulty in formulating relativistic partonlike equations
120403374
THREE-TRIPLET MODEL WITH DOUBLE SU(3) SYMMETRY
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)
121155180
DYON THREE-TRIPLET MODEL OF HADRONS.
118337761
Manifest dyality invariance in electrodynamics and the cabibbo-ferrari theory of magnetic monopoles
SummaryOne of the intrinsic symmetry properties of the Maxwell-Lorentz theory of electrodynamics is the invariance of the theory under « dyality » transformation, that is, a dual transformation on fieldsand sourcessimultaneously. In this paper we give a manifestly dyality-invariant formulation of electrodynamics. This is done by expressing the electromagnetic-field tensors in terms of an antisymmetric tensor of rank two, called a Hertz tensor, consisting of electric and magnetic Hertz vector potentials. An equation is derived which relates the electromagnetic fields when sources consist of electric charges only, magnetic charges only, and both. The present formalism provides a natural physical basis for the Cabibbo-Ferrari theory in which two four-vector potentials and a mixed gauge transformation between them are introduced.RiassuntoUna delle proprietà di simmetria intrinseca della teoria di Maxwell-Lorentz dell’elettrodinamica è l’invarianza della teoria rispetto alle trasformazioni di «dialità», cioè una trasformazione duale sui campie le sorgenticontemporaneamente. In questo articolo si espone una formulazione dell’elettrodinamica che è manifestamente invariante rispetto alla dialità. Si fà ciò esprimendo i tensori del campo elettromagnetico in termini di un tensore antisimmetrico di rango due, detto tensore di Hertz, consistente di potenziali del vettore di Hertz elettrico e magnetico. Si deduce un’equazione che mette in relazione i campi magnetici quando le sorgenti consistono di sole cariche elettriche, di sole cariche magnetiche, o di entrambe. Questo formalismo fornisce una naturale base fisica per la teoria di Cabibbo-Ferrari, in cui si introducono due potenziali quadrivettori e una trasformazione di gauge mista tra essi.РеэюмеОдно иэ свойств внутренней симметрии Максвелл-Лорентцевс кой теории злектродинамики представляет инвариантность теории относительно преобраэования «диальности», т.е. одновременное дуальное преобраэование полей и источников. В зтой статье мы приводим формулировку злектродинамики, обладаюшую явной диальной инвариантностью. Это достигается эа счет выражения тенэора злектромагнитного поля череэ антисимметричный тенэор второго ранга, наэываемый тенэором Герца, который состоит иэ злектрического и магнитного векторных потенциалов Герца. Выводится уравнение, которое свяэывает злектромагнитные поля, когда источники состоят только иэ злектрических эарядов, только иэ магнитных эарядов и тех и других. Предлагаемый формалиэм обеспечивает естественную фиэическую основу для теории Кабиббо-Феррари, в которой вводятся два четырех-векторных потенциала и смещанное калибровочное преобраэование между ними.