Searcharxiv⌕ Search

arXiv subjects

J. Alfaro

Publications and source records attributed to J. Alfaro.

35 records · Page 2Linked to original sources
arXiv2006

On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background

We show for the first time that the induced parity--even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light--like cosmic anisotropy axial--vector or for a time--like one, when in the presence of a bare photon mass.

hep-th↗
arXiv2003

On Non-Abelian Holonomies

We provide a method and the results for the calculation of the holonomy of a Yang-Mills connection in an arbitrary triangular path, in an expansion (developed here to fifth order) in powers of the corresponding segments. The results might have applications in generalizing to Yang-Mills fields previous calculations of the corrections to particle dynamics induced by loop quantum gravity, as well as in the field of random lattices.

hep-th↗
arXiv2002

Hadronic string, conformal invariance and chiral symmetry

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The `natural' candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally non-invariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the non-linear sigma model of pion interactions. At the next-to-leading order the O(p^4) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.

hep-th↗
arXiv2002

Quantum gravity and spin 1/2 particles effective dynamics

Quantum gravity phenomenology opens up the possibility of probing Planck scale physics. Thus, by exploiting the generic properties that a semiclassical state of the compound system fermions plus gravity should have, an effective dynamics of spin-1/2 particles is obtained within the framework of loop quantum gravity. Namely, at length scales much larger than Planck length and below the wave length of the fermion, the spin-1/2 dynamics in flat spacetime includes Planck scale corrections. In particular we obtain modified dispersion relations in vacuo for fermions. These corrections yield a time of arrival delay of the spin 1/2 particles with respect to a light signal and, in the case of neutrinos, a novel flavor oscillation. To detect these effects the corresponding particles must be highly energetic and should travel long distances. Hence Neutrino Bursts accompanying Gamma Ray Bursts or ultra high energy cosmic rays could be considered. Remarkably, future neutrino telescopes may be capable to test such effects. This paper provides a detailed account of the calculations and elaborates on results previously reported in a Letter. These are further amended by introducing a real parameter Upsilon aimed at encoding our lack of knowledge of scaling properties of the gravitational degrees of freedom.

hep-th↗
arXiv1999

Chiral lagrangians and the QCD string

We propose a method to derive the low-energy efective action of QCD assuming that the long-distance properties of strong interactions can be described by a string theory. We bypass the usual problems related to the existence of the tachyon and absence of the adequate Adler zero by using a sigma model approach where excitations above the correct (chirally non-invariant) QCD vacuum are included. Two-dimensional conformal invariance then implies the vanishing of the O(p^4) effective lagrangian coefficients. We discuss ways to go beyond this limit.

hep-th↗
arXiv1997

Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.

hep-th↗
arXiv1996

BRST Formulation of Partition Function Constraints

We show that constraints on the generating functional have direct BRST-extensions in terms of nilpotent operators $Δ$ that annihilate this generating functional, and which may be of arbitrarily high order. The free energy $F$ in the presence of external sources thus satisfies a ``Master Equation'' which is described in terms of a tower of higher antibrackets.

hep-th↗
arXiv1996

Algebra of Higher Antibrackets

We present a simplified description of higher antibrackets, generalizations of the conventional antibracket of the Batalin-Vilkovisky formalism. We show that these higher antibrackets satisfy relations that are identical to those of higher string products in non-polynomial closed string field theory. Generalization to the case of Sp(2)-symmetry is also formulated.

hep-th↗
arXiv1995

Non-Abelian Antibrackets

The $Δ$-operator of the Batalin-Vilkovisky formalism is the Hamiltonian BRST charge of Abelian shift transformations in the ghost momentum representation. We generalize this $Δ$-operator, and its associated hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly open algebra of any rank. We comment on the possible application of this formalism to closed string field theory.

hep-th↗
arXiv1995

Symmetries and the Antibracket

Requiring that a Lagrangian path integral leads to certain identities (Ward identities in a broad sense) can be formulated in a general BRST language, if necessary by the use of collective fields. The condition of BRST symmetry can then be expressed with the help of the antibracket, and suitable generalizations thereof. In particular, a new Grassmann-odd bracket, which reduces to the conventional antibracket in a special limit, naturally appears. We illustrate the formalism with various examples.

hep-th↗
arXiv1994

Generalized Lagrangian Master Equations

We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for the classical fields. Keeping the ghosts reveals the crucial role played by a natural connection on the space of fields.

hep-th↗
arXiv1993

Loop Equations for the d-dimensional n-Hermitian matrix model

We derive the loop equations for the d-dimensional n-Hermitian matrix model. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large $N$ the loop equations form a closed set. In particular we derive the loop equations for the $n=2^k$ matrix model recently proposed to describe the coupling of Two-dimensional quantum gravity to conformal matter with $c> 1$.

hep-th↗
arXiv1993

Origin of Antifields in the Batalin-Vilkovisky Lagrangian Formalism

The antifields of the Batalin-Vilkovisky Lagrangian quantization are standard antighosts of certain collective fields. These collective fields ensure that Schwinger-Dyson equations are satisfied as a consequence of the gauge symmetry algebra. The associated antibracket and its canonical structure appear naturally if one integrates out the corresponding ghost fields. An analogous Master Equation for the action involving these ghosts follows from the requirement that the path integral gives rise to the correct Schwinger-Dyson equations.

hep-th↗