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].
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.
118662643
Black Hole Entropy in Loop Quantum Gravity, Analytic Continuation, and Dual Holography
A new approach to black hole thermodynamics is proposed in Loop Quantum Gravity (LQG), by defining a new black hole partition function, followed by analytic continuations of Barbero-Immirzi parameter to $\gamma\in i\mathbb{R}$ and Chern-Simons level to $k\in i\mathbb{R}$. The analytic continued partition function has remarkable features: The black hole entropy $S=A/4\ell_P^2$ is reproduced correctly for infinitely many $\gamma= i\eta$, at least for $\eta\in\mathbb{Z}\setminus\{0\}$. The near-horizon Unruh temperature emerges as the pole of partition function. Interestingly, by analytic continuation the partition function can have a dual statistical interpretation corresponding to a dual quantum theory of $\gamma\in i\mathbb{Z}$. The dual quantum theory implies a semiclassical area spectrum for $\gamma\in i\mathbb{Z}$. It also implies that at a given near horizon (quantum) geometry, the number of quantum states inside horizon is bounded by a holographic degeneracy $d= e^{A/4\ell_P}$, which produces the Bekenstein bound from LQG. On the other hand, the result in arXiv:1212.4060 receives a justification here.
118545643
Canonical path-integral measures for Holst and Plebanski gravity: II. Gauge invariance and physical inner product
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from canonical framework and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory. This paper is divided into two parts, the first part is concerning the gauge invariance of the canonical path-integral measure for gravity from the reduced phase space quantization. We show that the path-integral measure is invariant under all the gauge transformations generated by all the constraints. These gauge transformations are the local symmetries of the gravity action, which is implemented without anomaly at the quantum level by the invariant path-integral measure. However, these gauge transformations coincide with the spacetime diffeomorphisms only when the equations of motion are imposed. But the path-integral measure is not invariant under spacetime diffeomorphisms, i.e. the local symmetry of spacetime diffeomorphisms become anomalous in the reduced phase space path-integral quantization. In the second part, we present a path-integral formula, which formally solves all the quantum constraint equations of gravity, and further results in a rigging map in the sense of refined algebraic quantization (RAQ). Then we give a formal path-integral expression of the physical inner product in loop quantum gravity (LQG). This path-integral expression is simpler than the one from reduced phase space quantization, since all the gauge-fixing conditions are removed except the time gauge. The resulting path-integral measure is different from the product Lebesgue measure up to a local measure factor containing both the spacetime volume element and the spatial volume element. This formal path-integral expression of the physical inner product can be a starting point for constructing a spin-foam model.
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.
119655234
On spinfoam models in large spin regime
We study the semiclassical behavior of Lorentzian Engle–Pereira–Rovelli–Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so-called, almost analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as Jf = λjf, where λ is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy mod . Our analysis results in a curvature expansion of the semiclassical low energy effective action from the spinfoam model, where the UV modifications of Einstein gravity appear as subleading high-curvature corrections.
119892209
Finite quantum electrodynamics: A field theory using an indefinite metric
A finite relativistic field theory of quantum electrodynamics is formulated; the theory involves as an essential element the use of an indefinite metric to remove the divergences. Two auxiliary fermion fields with anticommutation relations of opposite sign from the normal fermion field (electron) are coupled with the electron to the electromagnetic field in such a manner that any matrix element, calculated by a perturbation expansion, is finite. Although the new Lagrangian is not explicitly gauge invariant, the electromagnetic field is quantized by a method that yields a propagator in the true Landau gauge, and it is shown that this is sufficient to insure that the physical vector particles are zero-mass transverse quanta (i.e., photons). The physical electron mass and the fine-structure constant are put into the theory, leaving only the masses of the two auxiliary fields as parameters. The effects of mass and charge renormalization are calculated (the former using a technique involving a Taylor expansion in the mass), and are required to be small so that there is no explicit contradiction to the validity of the perturbation expansion. The anomalous magnetic moment of the electron and the differential and total cross sections for Compton scattering are calculated and compared with experiment. A range of the auxiliary mass parameters is found for which the predictions agree with experiment and for which the expansion criteria are satisfied. Thus, a finite quantum electrodynamics is accomplished.
120561444
Comment on the paper entitled «On the Poincaré noninvariance of a recent alternative to the Dirac equation»
120362684
TWO-COMPONENT POINCARE-INVARIANT EQUATIONS FOR MASSIVE CHARGED LEPTONS.
119565132
Gauge problem in quantum field theory
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.