Related papers: Immirzi parameter in the Barrett-Crane model?
We introduce a dual formulation of group field theories, making them a type of non-commutative field theories. In this formulation, the variables of the field are Lie algebra variables with a clear interpretation in terms of simplicial…
We discuss various features and details of two versions of the Barrett-Crane spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian model and second of the SL(2,C)-symmetric Lorentzian version in which all tetrahedra…
We study Fermi liquids with a Fermi surface that lacks continuous rotational invariance, and in the presence of an arbitrary quartic interaction. We obtain the expressions of the generalized static susceptibilities that measure the linear…
A long-wavelength, low-frequency effective theory is obtained from $t_1-t_2-J$ model. The action is written in terms of two-component bose spinor fields (CP^1 fields) and two spinless Fermi fields. The generalized CP^1 model is invariant…
BF theory is a topological theory that can be seen as a natural generalization of 3-dimensional gravity to arbitrary dimensions. Here we show that the coupling to point particles that is natural in three dimensions generalizes in a direct…
It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincare group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the…
The purpose of this Comment is to point out that the results presented in the appendix of M. Mondragon and M. Montesinos, J. Math. Phys. 47, 022301 (2006) provides a generic method so as to deal with cases as those of Section 6 of R.…
The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry…
The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors…
The paper is devoted to the study of BRST charge in perturbed two dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely…
This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General…
In this paper we research all possible finite-dimensional representations and corresponding values of the Barbero-Immirzi parameter contained in EPRL simplicity constraints by using Naimark's fundamental theorem of the Lorentz group…
Recent results in Local Regge Calculus are confronted with Spin Foam Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes it possible to associate a unique Spin $j_{h}$ with an hinge $h$, fulfilling one of the…
Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of…
We study a family of (possibly non topological) deformations of $BF$ theory for the Lie algebra obtained by quadratic extension of $\mathfrak{so}(3,1)$ by an orthogonal module. The resulting theory, called quadratically extended General…
In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the…
We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be…
Spatial stochastic processes that are modeled over the entire Earth's surface require statistical approaches that directly consider the spherical domain. Here, we extend the notion of intrinsic random functions (IRF) to model non-stationary…
In order to introduce an interaction between gravity and fermions in the Ashtekar-Barbero-Immirzi formalism without affecting classical dynamics a non-minimal term is necessary. The non-minimal term together with the Holst modification to…
It has been shown in [1] that a class of restricted spin foam models can feature a reduced spectral dimension of space-time. However, it is still an open question how curvature affects the flow of the spectral dimension. To answer this…