Related papers: Wick Rotation and Fermion Doubling in Noncommutati…
We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their…
The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless 2-component Dirac fermion extends this notion…
We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this…
Noncommutative gravity, based on a twist-deformation of the differential geometry of spacetime and a first-order formulation of the dynamics, requires additional gravitational degrees of freedom as well as an enlargement of the gauge group…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…
The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum…
We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing 4-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by…
We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with…
Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and…
We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes'…
We construct a positive complexifier, differentiable almost everywhere on the classical phase space of real triads and $SU(2)$ connections, which generates a Wick Transform from Euclidean to Lorentzian gravity everywhere except on a phase…
We discuss the generic geometric properties of metrics $\widehat {g}_{ab}$ constructed from Lorentzian metric $g_{ab}$ and a nowhere vanishing, hypersurface orthogonal, timelike vector field $u^a$. The metric ${\widehat g}_{ab}$ has…
We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic…
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
This article investigates the construction of fermions and the formulation of the Standard Model of particle physics in a theory in which the Lorentz signature emerges from an underlying microscopic purely Euclidean $SO(4)$ theory.…
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non- canonical transformations in general also change the statistics of the operators involved. In…
The Green function of the quark-antiquark system in the confining background field is analysed using the Feynman-Schwinger formalism. The Hamiltonian for the case of massive spinning quarks is obtained in the form containing essentially…
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion…
Using Ashtekar variables, we analyze Lorentzian and Euclidean gravity in vacuum up to a constant conformal transformation. We prove that the reality conditions are invariant under a Wick rotation of the time, and show that the compatibility…