Non-local Lee-Wick modes in the fermionic Myers-Pospelov model
The need for a more fundamental theory at high energies has been justified in many contexts. Divergences in quantum field theory, singularities in gravity and having a unified quantum framework for all forces, are some of them. A consequence arising from this consideration, which has been extensively studied, is the possibility of having Lorentz invariance violation given in the form of effective corrections . This idea naturally leads to new extensions of the standard model and modified dispersion relations for particles which may to be detected in sensitive experiments . In this contexts the Myers-Pospelov theory is a model that introduces Lorentz invariance violation through dimension five operators [3, 4]. The breakdown of Lorentz symmetry that is included in the scalar, fermion and gauge sectors is characterized by an external timelike four-vector nμ defining a preferred reference frame. Experimental bounds for this model have been studied in several phenomena, such as synchrotron radiation , gamma ray bursts [6], neutrino physics [7], radiative corrections . generic backgrounds [9, 10], and others [11]. In recent years and from a different approach, theories with higher time-derivatives have been proposed as an extension of the standard model of particles . One of the main motivations is that these theories soften the ultraviolet behavior of the quantum field theory, and hence problems like the hierarchy puzzle seems to be solved. Despite these theories contain negative norm states [13] the theoretical consistency were established many years ago . Although unitarity is maintained, the price to pay is the lost of microcausality . The lost of microcausality and higher time derivatives are ingredients present in Myers-Pospelov theory. Then, it seems natural to wonder for the content of Lee-Wick modes in the Myers-Pospelov theory. In this work our main purpose is to rigorously establish these connection. The layout of this work is the following. In Sec. II we introduce the fermionic Myers and Pospelov model where we found the exact dispersion relation and we compute the corresponding eigenspinor in any background. In Sec. III we quantize the theory and we show explicitly the connection between the Myers-Pospelov model and Lee-Wick theories. In Sec. IV we discuss the origin of violations of microcausality and give the conclusions and final comments.

title: Unitarity, ghosts and nonminimal terms in Lorentz violating QED
abstract: The unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.

title: Unitarity in higher-order Lorentz-invariance violating QED
abstract: The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.

title: Unitarity in a Lorentz symmetry breaking model with higher-order operators
abstract: We analyze the unitarity of a modified QED with higher-order terms that violate Lorentz symmetry. We make an explicit calculation to verify unitarity at the one-loop level. As expected we find negative norm states that could in principle lead to a violation of unitarity. However, we show that these states become massive in Euclidean space and do not contribute to the discontinuity.

title: Higher time derivatives, stability and Fermi Statistics
abstract: We show that statistics is crucial for the instability problem derived from higher time derivatives. In fact, and contrary to previous statements, we check that when dealing with Fermi systems, the Hamiltonian is well bounded and the quantum states are normalizable. Although, ghost states are still present, they do not affect unitarity under certain conditions. We first analyze a quantum oscillator involving Grassman variables and then we generalize it to a Dirac field. Finally, we discuss some physical implications

title: Alternative approaches to Lorentz violation invariance in loop quantum gravity inspired models
abstract: Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of phase-space variables. In this note we show that such alternative is inconsistent with (i) the choice of variables in the regularized underlying quantum theory from which the effective theories are derived and (ii) the application of the correspondence principle. A consistent choice will violate standard Lorentz invariance, with the exception of trivial zero Planck scale corrections which are allowed by the analysis. Thus, for nontrivial corrections, to preserve a relativity principle in these models, the linear realization of Lorentz symmetry should be extended or superseded.

title: Flexibility in the ABC transporter MsbA: Alternating access with a twist
abstract: ATP-binding cassette (ABC) transporters are integral membrane proteins that translocate a wide variety of substrates across cellular membranes and are conserved from bacteria to humans. Here we compare four x-ray structures of the bacterial ABC lipid flippase, MsbA, trapped in different conformations, two nucleotide-bound structures and two in the absence of nucleotide. Comparison of the nucleotide-free conformations of MsbA reveals a flexible hinge formed by extracellular loops 2 and 3. This hinge allows the nucleotide-binding domains to disassociate while the ATP-binding half sites remain facing each other. The binding of the nucleotide causes a packing rearrangement of the transmembrane helices and changes the accessibility of the transporter from cytoplasmic (inward) facing to extracellular (outward) facing. The inward and outward openings are mediated by two different sets of transmembrane helix interactions. Altogether, the conformational changes between these structures suggest that large ranges of motion may be required for substrate transport.

title: Structure of the ABC Transporter MsbA in Complex with ADP·Vanadate and Lipopolysaccharide
abstract: Select members of the adenosine triphosphate (ATP)-binding cassette (ABC) transporter family couple ATP binding and hydrolysis to substrate efflux and confer multidrug resistance. We have determined the x-ray structure of MsbA in complex with magnesium, adenosine diphosphate, and inorganic vanadate (Mg·ADP·Vi) and the rough-chemotype lipopolysaccharide, Ra LPS. The structure supports a model involving a rigid-body torque of the two transmembrane domains during ATP hydrolysis and suggests a mechanism by which the nucleotide-binding domain communicates with the transmembrane domain. We propose a lipid “flip-flop” mechanism in which the sugar groups are sequestered in the chamber while the hydrophobic tails are dragged through the lipid bilayer.