Note on gauge invariance and causal propagation

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the normal state of the copper-oxide high-temperature superconductors, drastic deviations from the Fermi liquid picture are obtained, highlighted by a pseudogap, broad spectral features and T-linear resistivity. A successful theory in this context must confront the highly constraining scaling argument which establishes that all 4-Fermi interactions are irrelevant (except for pairing) at a Fermi surface. This argument lays plain that new low-energy degrees of freedom are necessary. This paper focuses on the series of experiments on copper-oxide superconductors which reveal that the number of low-energy addition states per electron per spin exceeds unity, in direct violation of the key Fermi liquid tenet. These experiments point to new degrees of freedom, not made out of the elemental excitations, as the key mechanism by which Fermi liquid theory breaks down in the cuprates. A recent theoretical advance which permits an explicit integration of the high-energy scale in the standard model for the cuprates reveals the source of the new dynamical degrees of freedom at low energies, a charge 2e bosonic field which has nothing to do with pairing but rather represents the mixing with the high-energy scales. We demonstrate explicitly that at half-filling, this new degree of freedom provides a dynamical mechanism for the generation of the charge gap and antiferromagnetism in the insulating phase. At finite doping, many of the anomalies of the normal state of the cuprates including the pseudogap, T-linear resistivity and the mid-infrared band are reproduced. A possible route to superconductivity is explored.

Thermodynamic metric usually works only for those black holes with more than one conserved charge, thereby excluding the Schwarzschild black hole. In this paper, however, different versions of thermodynamic metric are computed and compared for the Schwarzschild-like black hole by introducing new degrees of freedom. These new degrees of freedom have two purposes. First, the deformed metric may be treated offshell to the ordinary Schwarzschild black hole, and onshell physics corresponds to the submanifold by gauge fixing of this additional degree of freedom. In particular, the thermal Ricci scalar for the Schwarzschild black hole, though different for various deformations, can be obtained by switching off the deformation. Second, while deformed metric is treated onshell, a divergent Ricci scalar may signal an exotic phase in which new physical degrees of freedom manifest. This paper considers the new degree of freedom as the running Newton constant, a cutoff scale for regular black holes, a noncommutative deformation or the deformed parameter in the nonextensive Tsallis–Rènyi entropy.

Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of some screening mechanisms, thereby threatening the viability of these modified gravity theories. Specifically, we show that the waves produced in the symmetron model can increase the amplitude of the fifth force and the parametrized post Newtonian parameters by several orders of magnitude.

Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics remain open to date. The purpose of this thesis is to explore classical and quantum gravity in order to improve our understanding of different aspects of gravity, such as dark matter, gravitational waves and ination. We focus on the class of higher derivative gravity theories as they naturally arise after the quantization of general relativity in the framework of effective field theory. The inclusion of higher order curvature invariants to the action always come in the form of new degrees of freedom. From this perspective, we introduce a new formalism to classify gravitational theories based on their degrees of freedom and, in light of this classification, we argue that dark matter is no different from modified gravity. Additional degrees of freedom appearing in the quantum gravitational action also affect the behaviour of gravitational waves. We show that gravitational waves are damped due to quantum degrees of freedom and we investigate the backreaction of these modes. The implications for gravitational wave events, such as the ones recently observed by the Advanced LIGO collaboration, are also discussed. The early universe can also be studied in this framework. We show how ination can be accommodated in this formalism via the generation of the Ricci scalar squared, which is triggered by quantum effects due to the non-minimal coupling of the Higgs boson to gravity, avoiding instability issues associated with Higgs ination. We argue that the non-minimal coupling of the Higgs to the curvature could also solve the vacuum instability issue by producing a large effective mass for the Higgs, which quickly drives the Higgs field back to the electroweak vacuum during ination.

Recent advances have made it viable to fabricate optical surfaces that are not rotationally symmetric using a new generation of diamond-turning machines. This new fabrication capability allows for surfaces whose departure from a sphere varies both radially and azimuthally in the aperture to be machined into an optical surface. This new degree of freedom allows for the design of unobscured optical systems that are truly non-symmetric by tilting the optical surfaces themselves. With this new design degree of freedom, the aperture and field of view can be pushed to yield an order of magnitude increase in aerial coverage over current production while maintaining a compact solution. In one particular case, to be presented, a diffraction limited (< λ/10), long wave infrared (LWIR), F/1.9, 10° full field of view sensor telescope is designed by introducing these non-symmetric surfaces into the optical surface prescription.

The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. Quite generally, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behaviour. On one hand, often these new degrees of freedom have negative kinetic energy, which implies that the theory is plagued by ghost instabilities. On the other hand, for a modified gravity theory to be phenomenologically viable it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider two different models, the Cascading DGP and the dRGT massive gravity, which are candidates for viable models to modify gravity at very large distances. Regarding the Cascading DGP model, we consider the minimal (6D) set-up and we perform a perturbative analysis at first order of the behaviour of the gravitational field and of the branes position around background solutions where pure tension is localized on the 4D brane. We consider a specific realization of this set-up where the 5D brane can be considered thin with respect to the 4D one. We show that the thin limit of the 4D brane inside the (already thin) 5D brane is well defined, at least for the configurations that we consider, and confirm that the gravitational field on the 4D brane is finite for a general choice of the energymomentum tensor. We also confirm that there exists a critical tension which separates background configurations which possess a ghost among the perturbation modes, and background configurations which are ghost-free. We find a value for the critical tension which is different from the value which has been obtained in the literature; we comment on the difference between these two results, and perform a numeric calculation in a particular case where the exact solution is known to support the validity of our analysis. Regarding the dRGT massive gravity, we consider the static and spherically symmetric solutions of these theories, and we investigate the effectiveness of the Vainshtein screening mechanism. We focus on the branch of solutions in which the Vainshtein mechanism can occur, and we truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. Moreover, we analyze in detail in which cases the solutions match in an intermediate region. We show that asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space of the theory where global solutions do not exist, and characterize precisely in which regions the Vainshtein mechanism takes place.

We are interested in a gauge invariant coupling between four-dimensional Yang–Mills field and a three-brane that can fluctuate into higher dimensions. For this we interpret the Yang–Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional spacetime under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original spacetime . The presence of the brane becomes entirely invisible, expect for the mass.

We construct a proof of the second law of thermodynamics in an arbitrary diffeomorphism invariant theory of gravity working within the approximation of linearized dynamical fluctuations around stationary black holes. We achieve this by establishing the existence of an entropy current defined on the horizon of the dynamically perturbed black hole in such theories. By construction, this entropy current has non-negative divergence, suggestive of a mechanism for the dynamical black hole to approach a final equilibrium configuration via entropy production as well as the spatial flow of it on the null horizon. This enables us to argue for the second law in its strongest possible form, which has a manifest locality at each space-time point. We explicitly check that the form of the entropy current that we construct in this paper exactly matches with previously reported expressions computed considering specific four derivative theories of higher curvature gravity. Using the same set up we also provide an alternative proof of the physical process version of the first law applicable to arbitrary higher derivative theories of gravity.

In this paper, based on the AdS2/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z→∞). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z=5 fixed point.

The use of a continuously varying index of refraction provides new degrees of freedom in the design of lens systems. By use of the third-order aberration theory developed by Sands, the effectiveness of these new degrees of freedom in correcting third-order aberrations is determined. After the theory is cast into a form suitable for a computer, two major designs are done. The first is a singlet with an axial gradient that is corrected for third-order spherical and chromatic aberrations and has no third-order distortion. A radial gradient is used in a singlet to correct all third-order monochromatic aberrations except Petzval curvature of field. The results of the study indicate that axial gradients have the same effect as aspheric surfaces for third-order aberrations. The study also shows that radial gradients are more effective in aberration correction than axial gradients and have a greater potential in lens design.

Solar control tunable Lippmann holowindows

The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information.In this paper, we study generalized Wronskians of the Baker–Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg–Shih relation, we propose that these new degrees of freedom can be identified as FZZT-Cardy branes in Liouville theory. This means that FZZT-Cardy branes are the bound states of elemental FZZT branes (i.e. the twisted fermions) rather than the bound states of principal FZZT-brane (i.e. the resolvent operator).

This article demonstrates several approaches to the vehicle energy consumption and tailpipe emission reduction opportunities. The article leverages the vehicle storage dynamics through smart and personalized optimization and control approaches in the context of connected vehicles. Recent advances in vehicle connectivity and automation have brought unprecedented information richness and new degrees of freedom that can be synergized with insightful understanding of vehicle powertrain and aftertreatment physical systems. Vehicle automation also provides new degrees of freedom that can be further leveraged by the vehicle control systems to improve vehicle energy efficiency and reduce tailpipe emissions. While vehicle automation levels probably will keep increasing, humans will still be involved in vehicle operations at various levels for the foreseeable future. The prediction of future vehicle’s power demand based on vehicle connectivity can significantly benefit tailpipe emission reductions and fuel economy.

The Thomas-Whitehead projective gravity action is a gravitational theory that reduces to the Einstein-Hilbert functional in a particular limit. However, unlike Einstein’s theory of general relativity, the Thomas-Whitehead functional is invariant under projective transformations, is integrated over the determinant line bundle of the underlying manifold, and possesses a new degree of freedom, called the Diffeomorphism field, whose infinitesimal 1-dimensional coordinate transformation recovers the coadjoint action of a Virasoro coadjoint element. We generalize the Thomas-Whitehead projective gravity action to a graded setting. Background material on the theory of supermanifolds is provided.

The integration of dissimilar materials in heterostructures has long been acornerstone of modern materials science-seminal examples are 2D materials and van der Waals heterostructures. Recently, new methods have been developed that enable the realization of ultrathin freestanding oxide films approaching the 2D limit. Oxides offer new degrees of freedom, due to the strong electronic interactions, especially the 3d orbital electrons, which give rise to rich exotic phases. Inspired by this progress, a new platform for assembling freestanding oxide thin films with different materials and orientations into artificial stacks with heterointerfaces is developed. It is shown that the oxide stacks can be tailored by controlling the stacking sequences, as well as the twist angle between the constituent layers with atomically sharp interfaces, leading to distinct moiré patterns in the transmission electron microscopy images of the full stacks. Stacking and twisting is recognized as a key degree of structural freedom in 2D materials but, until now, has never been realized for oxide materials. This approach opens unexplored avenues for fabricating artificial 3D oxide stacking heterostructures with freestanding membranes across a broad range of complex oxide crystal structures with functionalities not available in conventional 2D materials.