Magnetic properties of the Larkin-Ovchinnikov-Fulde-Ferrell superconducting phase

We compute, at the first order in the fine structure constant, the parameters of the electromagnetic Lagrangian for the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell phase in Quantum Chromodynamics (QCD) and in condensed matter. In particular we compute for QCD with two flavors the dielectric and the magnetic permeability tensors, and for condensed matter superconductors the penetration depth of external magnetic fields.Comment: 12 page

Algebraic treatment of compactification on noncommutative tori

In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori. The main tool used for this analysis is the algebra A(Z^D) of the projective representations of the abelian group Z^D. We exhibit the explicit solutions in the space of the multiplication algebra of A(Z^D), that is the algebra generated by right and left multiplications.Comment: 8 pages, Latex, shortened version as accepted for publication in Physics Letter

Projective Group Algebras

In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the $M$ theory on noncommutative tori. This turns out to be an interesting field of applications, since the space $\hat G$ of the equivalence classes of the vector unitary irreducible representations of the group under examination becomes, in the projective case, a prototype of noncommuting spaces. For vector representations the algebraic integration is equivalent to integrate over $\hat G$. However, its very definition is related only at the structural properties of the group algebra, therefore it is well defined also in the projective case, where the space $\hat G$ has no classical meaning. This allows a generalization of the usual group harmonic analysis. A particular attention is given to abelian groups, which are the relevant ones in the compactification problem, since it is possible, from the previous results, to establish a simple generalization of the ordinary calculus to the associated noncommutative spaces.Comment: 24 pages, Late

A Theory of algebraic integration

In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such spaces. We consider this problem and we show how to define an integration which respects the physical principle of composition of the probability amplitudes for a very large class of algebras.Comment: 7 pages, LaTeX (or Latex, etc). Contribution to the Path Integral from peV to TeV Conference, Florence-Italy, August 25-29, 199

Anisotropic Color Superconductivity

We discuss the possibility that in finite density QCD an anisotropic phase is realized. This case might arise for quarks with different chemical potential and/or different masses. In this phase crystalline structures may be formed. We consider this possibility and we describe, in the context of an effective lagrangian, the corresponding phonons as the Nambu-Goldstone bosons associated to the breaking of the space symmetries.Comment: LaTex 17 pages, 6 figures. Contributed paper to the International Workshop SCGT 02 "Strong Coupling Gauge Theories and Effective Field Theories", 10-13 December 2002, Nagoya, Japa

Duality in the Color Flavor Locked Spectrum

We analyze the spectrum of the massive states for the color flavor locked phase (CFL) of QCD. We show that the vector mesons have a mass of the order of the color superconductive gap $\Delta$. We also see that the excitations associated with the solitonic sector of the CFL low energy theory have a mass proportional to $F^2_{\pi}/\Delta$ and hence are expected to play no role for the physics of the CFL phase for large chemical potential. Another interesting point is that the product of the soliton mass and the vector meson mass is independent of the gap. We interpret this behavior as a form of electromagnetic duality in the sense of Montonen and Olive. Our approach for determining the properties of the massive states is non-perturbative in nature and can be applied to any theory with multiple scales.Comment: RevTeX4, 4 page

Color superconductivity in high density QCD

In this contributed paper the gapless phases of QCD are discussed.Comment: Contributed paper to the Conference "Quark confinement ant the Hadron Spectrum VI 2004". Latex, 3 page

On the Ground State of QCD inside a Compact Stellar Object

We describe the effects of the strange quark mass and of the color and electric neutrality on the superconducing phases of QCD.Comment: Invited talk at the 2006 International Workshop SCGT 06 "Origin of Mass and Strong Coupling Gauge Theories" 21-24 November 2006, Nagoya, Japan. Latex file 15 pages. 6 figure