Universally coupled massive gravity, II: Densitized tetrad and cotetrad theories

Einstein’s equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein’s equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.     

Lorentz invariance on trial in the weak decay of polarized atoms

The invariance of the laws of physics under Lorentz transformations is one of the most fundamental principles underlying our current understanding of nature. In theories trying to unify the Standard Model with quantum gravity, this invariance may be broken, and dedicated high-precision experiments at low energy could be used to reveal such suppressed signals from the Planck scale. We will test Lorentz invariance searching for a dependence of the decay rate of spin-polarized nuclei on the daily, yearly or deliberate re-orientation of the spin. Observation of such a dependence would imply a breakdown of Lorentz invariance.     

Lorentz invariance on trial in the weak decay of polarized atoms

One of the most fundamental principles underlying our current understanding of nature is the invariance of the laws of physics under Lorentz transformations. Theories trying to unify the Standard Model with quantum gravity suggest that this invariance may be broken by the presence of Lorentz-violating background fields. Dedicated high-precision experiments at low energies could observe such suppressed signals from the Planck scale. At KVI, a test on Lorentz invariance of the weak interaction is performed searching for a dependence of the decay rate of spin-polarized nuclei on the orientation of their spin with respect to a fixed absolute galactical reference frame. An observation of such a dependence would imply a violation of Lorentz invariance.     

Inverse turbulent cascades and conformally invariant curves

We offer a new example of conformal invariance (local scale invariance) far from equilibrium-the inverse cascade of surface quasigeostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa). The diffusivity is close to kappa=4, that is, isotemperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are shown to agree with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.     

Lorentz invariance and quantum gravity: an additional fine-tuning problem?

Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space time at around the Planck length, 1.6x10(-35) m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.     

Hierarchical order of Galilei and Lorentz invariance in the structure of matter

The structure of matter shows a hierarchical order: (1) from Lorentz invariance in high-energy physics; (2) to Galilei invariance in the low-energy nonrelativistic limit of high-energy physics; and (3) again to Lorentz invariance in condensed matter physics (where the velocity of sound takes the place of the velocity of light). The hierarchical order can be continued downward further to: (4) non-relativistic (velocity small compared to the velocity of sound) condensed matter excitons, obeying Galilei invariance; and (5) to excitonic matter obeying Lorentz invariance with an excitonic matter sound velocity. It was previously conjectured that Lorentz invariance of high-energy physics is preceded by Galilei invariance at the Planck scale. Still further, the conjectured Galilei invariance at the Planck scale may be the result of an underlying five-dimensional non-Euclidean conform invariant metric structure, with three spatial and two time dimensions, compactified onto three spatial and one time dimension.     

Cold atom clock test of Lorentz invariance in the matter sector

We report on a new experiment that tests for a violation of Lorentz invariance (LI), by searching for a dependence of atomic transition frequencies on the orientation of the spin of the involved states (Hughes-Drever type experiment). The atomic frequencies are measured using a laser cooled 133Cs atomic fountain clock, operating on a particular combination of Zeeman substates. We analyze the results within the framework of the Lorentz violating standard model extension (SME), where our experiment is sensitive to a largely unexplored region of the SME parameter space, corresponding to first measurements of four proton parameters and improvements by 11 and 13 orders of magnitude on the determination of four others. In spite of the attained uncertainties, and of having extended the search into a new region of the SME, we still find no indication of LI violation.     

Test of CPT and Lorentz invariance from muonium spectroscopy

Following a suggestion from Kostelecky et al., we evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts deltanu(12) and deltanu(34) to nu(12) and nu(34), the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anticorrelated oscillations in nu(12) and nu(34) at the Earth's sidereal frequency. No time dependence was found in nu(12) or nu(34) at the level of 20 Hz, limiting the size of some CPT and Lorentz-violating parameters at the level of 2x10(-23) GeV.     

Scheme dependence of quantum gravity on de Sitter background

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.     

Linear derivative Cartan formulation of general relativity

Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin connection variables and auxiliary two-form fields. In the systematic study of all possible embeddings of Einstein gravity into that formulation with auxiliary fields, the introduction of a “bi-complex” algebra possesses crucial technical advantages. Certain components of the new two-form fields directly provide canonical momenta for spatial components of all Cartan variables, whereas the remaining ones act as Lagrange multipliers for a large number of constraints, some of which have been proposed already in different, less radical approaches. The time-like components of the Cartan variables play that role for the Lorentz constraints and others associated to the vierbein fields. Although also some ternary ones appear, we show that relations exist between these constraints, and how the Lagrange multipliers are to be determined to take care of second class ones. We believe that our formulation of standard Einstein gravity as a gauge theory with consistent local Poincaré algebra is superior to earlier similar attempts.Received: 24 January 2005, Published online: 8 June 2005     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

One Fermion-Loop Correction and Supersymmetry in the Heterotic String Theory

(2, 0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Special care is taken to study the cancellation of local Lorentz and gauge anomalies caused by one fermion-loop..My computation shows that local counterterms which simultaneously restore local Lorentz and gauge invariance of the sigma model do not satisfy the criteria of (2, 0) supersymmetry. But local counterterms and the non-local part of one loop effective action are together invariant under the (2, 0) supersymmetry transformation.     

A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics.     

Anyons from strings

The Nambu-Goto string in a three-dimensional (3D) Minkowski spacetime is quantized preserving Lorentz invariance and parity. The spectrum of massive states contains anyons. An ambiguity in the ground state energy is resolved by the 3D N=1 Green-Schwarz superstring, which has massless ground states describing a dilaton and dilatino, and first-excited states of spin 1/4.     

New theory of Lorentz violation from a general principle

We report that a general principle of physical independence of mathematical background manifolds brings a replacement of common derivative operators by co-derivative ones. Then we obtain a new Lagrangian for the ordinary minimal standard model with supplementary terms containing the Lorentz invariance violation information measured by a new matrix, denoted as the Lorentz invariance violation matrix. We thus provide a new fundamental theory to study Lorentz invariance violation effects consistently and systematically.     

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.     

CPT-symmetry studies with antihydrogen

Various approaches to physics beyond the Standard Model can lead to small violations of CPT invariance. Since CPT symmetry can be measured with ultra-high precision, CPT tests offer an interesting phenomenological avenue to search for underlying physics. We discuss this reasoning in more detail, comment on the connection between CPT and Lorentz invariance, and review how CPT breaking would affect the (anti)hydrogen spectrum.     

On the difference between Poincaré and Lorentz gravity

The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy–momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.