Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing

The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in Weinberg-Salam theory, particularly in the context of the Electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the Electroweak Z string, through the ``bag'' phenomenon described by Watkins and Vachaspati. (Recently cosmic strings have climbed back into interest due to new evidence). Sourced by static embedded strings, an internal space analogy of Cartan's torsion is drawn, and a possible Higgs-force-like `gravitational' effect of this non-propagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the $\nu_R$ is non-zero in the physical vacuum.Comment: 42 page

Scattering Polarization in the Presence of Magnetic and Electric Fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the $Q/I$ profiles and rotation of the plane of polarization in the $U/I$ profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady state and time varying electric fields that surround radiating atoms in Solar atmospheric layers.Comment: 41 pages, 6 figure

String Geometry and the Noncommutative Torus

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra A and the noncommutative torus. We show that the (truncated) tachyon subalgebra of A is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding even real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;Z) Morita equivalences between $d$-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang-Mills gauge theory minimally coupled to massive Dirac fermion fields.Comment: 37 pages, LaTeX. Major revisions in section 3. Other minor revisions in the rest of the paper, references adde

On the Dirac Eigenvalues as Observables of the on-shell N=2 D=4 Euclidean Supergravity

We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean supergravity. The covariant phase space of the theory is defined as as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.Comment: 10 pages, LATeX fil

Non-abelian instantons on a fuzzy four-sphere

We study the compatibility between the $BPST SU(2)$ instanton and the fuzzy four-sphere algebra. By using the projective module point of view as an intermediate step, we are able to identify a non-commutative solution of the matrix model equations of motion which minimally extends the SU(2) instanton solution on the classical sphere $S^4$. We also propose to extend the non-trivial second Chern class with the five-dimensional noncommutative Chern-Simons term

Lattices and Their Continuum Limits

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space $M$. The correct framework is that of projective systems. The projective limit is a universal space from which $M$ can be recovered as a quotient. We dualize the construction to approximate the algebra ${\cal C}(M)$ of continuous functions on $M$. In a companion paper we shall extend this analysis to systems of noncommutative lattices (non Hausdorff lattices).Comment: 11 pages, 1 Figure included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the list of author

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.Comment: v2: 38 pages; completely rewritten. The crucial difference with respect to the first version is that in the present one the quantum four-sphere, the base space of the fibration, is NOT a quantum homogeneous space. This has important consequences and led to very drastic changes to the paper. To appear in CM

Nonthermal hard X-ray excess in the Coma cluster: resolving the discrepancy between the results of different PDS data analyses

The detection of a nonthermal excess in the Coma cluster spectrum by two BeppoSAX observations analyzed with the XAS package (Fusco-Femiano et al.) has been disavowed by an analysis (Rossetti & Molendi) performed with a different software package (SAXDAS) for the extraction of the spectrum. To resolve this discrepancy we reanalyze the PDS data considering the same software used by Rossetti & Molendi. A correct selection of the data and the exclusion of contaminating sources in the background determination show that also the SAXDAS analysis reports a nonthermal excess with respect to the thermal emission at about the same confidence level of that obtained with the XAS package (~4.8sigma). Besides, we report the lack of the systematic errors investigated by Rossetti & Molendi and Nevalainen et al. taking into account the whole sample of the PDS observations off the Galactic plane, as already shown in our data analysis of Abell 2256 (Fusco-Femiano, Landi & Orlandini). All this eliminates any ambiguity and confirms the presence of a hard tail in the spectrum of the Coma cluster.Comment: 12 pages, 2 figures. Accepted for publication in ApJ Letter

Coronal emission lines as thermometers

Coronal emission line intensities are commonly used to measure electron temperatures using emission measure and/or line ratio methods. In the presence of systematic errors in atomic excitation calculations and data noise, the information on underlying temperature distributions is fundamentally limited. Increasing the number of emission lines used does not necessarily improve the ability to discriminate between different kinds of temperature distributions.Comment: Accepted by ApJ, November 200