Paola Giacconi

Lorentz and CPT violations from Chern-Simons modifications of QED

The possibility of a small modification of spinor Quantum Electro-Dynamics is reconsidered, in which Lorentz and CPT non-covariant kinetic terms for photons and fermions are present. The corresponding free field theory is carefully discussed. The finite one-loop parity-odd induced effective action is unambiguously calculated using the physical cutoff method, which manifestly encodes the maximal residual symmetry group allowed by the presence of the Lorentz and CPT breaking axial-vector. This very same induced effective action, which is different from those ones so far quoted in the Literature, is also re-derived by means of the dimensional regularization, provided the maximal residual symmetry is maintained in the enlarged D-dimensional space-time. As a consequence, it turns out that the requirement of keeping the maximal residual symmetry at the quantum level just corresponds to the physical renormalization prescription which naturally fixes the one-loop parity-odd induced effective action.

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.

BARE AND INDUCED LORENTZ AND CPT INVARIANCE VIOLATIONS IN QED

We consider QED in a constant axial vector background (AEther). Further Lorentz invariance violations (LIV) might occur owing to radiative corrections. The phenomenology of this model is studied, clarifying issues related to the various regularizations employed, with a particular emphasis on the induced photon mass. To this concern, it is shown that in the presence of LIV dimensional regularization may produce a radiatively induced finite photon mass. The possible physical role of the large momentum cutoff is elucidated and the finite temperature radiative corrections are evaluated. Finally, various experimental bounds on the parameters of the model are discussed.

Anomalous positron excess from Lorentz-violating QED

We entertain the idea that a suitable background of cold (very low momentum) pseudoscalar particles or condensate, may trigger a background that effectively generates Lorentz-invariance violation. This ae ther-like background induces a Chern-Simons modification of QED. Physics is different in different frames and, in the rest frame of the pseudoscalar background, high momentum photons can decay into pairs. The threshold for such decay depends quadratically on the rest mass of the particles. This mechanism could explain in a natural way why antiprotons are absent in recent cosmic ray measurements. A similar signal could be used as a probe of pseudoscalar condensation in heavy ion collisions.

Domain wall generation by fermion self-interaction and light particles

A possible explanation for the appearance of light fermions and Higgs bosons on the four-dimensional domain wall is proposed. The mechanism of light particle trapping is accounted for by a strong self-interaction of five-dimensional pre-quarks. We obtain the low-energy effective action which exhibits the invariance under the so called τ-symmetry. Then we find a set of vacuum solutions which break that symmetry and the five-dimensional translational invariance. One type of those vacuum solutions gives rise to the domain wall formation with consequent trapping of light massive fermions and Higgs-like bosons as well as massless sterile scalars, the so-called branons. The induced relations between low-energy couplings for Yukawa and scalar field interactions allow to make certain predictions for light particle masses and couplings themselves, which might provide a signature of the higher dimensional origin of particle physics at future experiments. The manifest translational symmetry breaking, eventually due to some gravitational and/or matter fields in five dimensions, is effectively realized with the help of background scalar defects. As a result the branons acquire masses, whereas the ratio of Higgs and fermion (presumably top-quark) masses can be reduced towards the values compatible with the present-day phenomenology. Since the branons do not couple to fermions and the Higgs bosons do not decay into branons, the latter ones are essentially sterile and stable, what makes them the natural candidates for the dark matter in the Universe.

Decay in a uniform field: an exactly solvable model

We investigate the time evolution of the decay (or ionization) probability of a D-dimensional model atom (D = 1, 2, 3) in the presence of a uniform (i.e., static and homogeneous) background field. The model atom consists in a non-relativistic point particle in the presence of a point-like attractive well. It is shown that the model exhibits infinitely many resonances leading to possible deviations from the naive exponential decay law of the non-decay (or survival) probability of the initial atomic quantum state. Almost stable states exist due to the presence of the attractive interaction, no matter how weak it is. Analytic estimates as well as numerical evaluation of the decay rates are explicitly given and discussed.

Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene

We study one-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the relationship among the invariance of the theory under large gauge transformations, the appearance of Chern–Simons terms and of different Berrys phases. In the case of a purely electric background field, we show that the effective Lagrangian is independent of the chemical potential and of the temperature. More interesting, we show that the minimal conductivity, as predicted by the quantum field theory, is the right multiple of the conductivity quantum and is, thus, consistent with the value measured for graphene, with no extra factor of π in the denominator.

Brane world generation by matter and gravity

We present a non-compact 4 + 1 dimensional model with a local strong four-fermion interaction supplementing it with gravity. In the strong coupling regime it reveals the spontaneous translational symmetry breaking which eventually leads to the formation of domain walls, or thick 3-branes, embedded in the AdS5 manifold. To describe this phenomenon we construct the appropriate low-energy effective Action and find kink-like vacuum solutions in the quasi-flat riemannian metric. We discuss the generation of ultra-low-energy 3 + 1 dimensional physics and we establish the relation among the bulk five dimensional gravitational constant, the brane Newtons constants and the curvature of AdS5 space-time. The plausible relation between the compositeness scale of the scalar matter and the symmetry breaking scale is shown to support the essential decoupling of branons, the scalar fluctuations of the brane, from the Standard Model matter, supporting their possible role in the dark matter saturation. The induced cosmological constant on the brane does vanish due to exact cancellation of matter and gravity contributions.

The quantum Hall effect in graphene samples and the relativistic Dirac effective action

We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two-dimensional (2D) spatial region, in the presence of a uniform magnetic field perpendicular to the 2D plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.

Scattering amplitude in the Aharonov-Bohm gauge field.

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time independent formalism. The result is valid also in the backward and forward directions as well as for any choice of the boundary conditions on the wave function at the flux tube position.