Thiemann transform for gravity with matter fields

The generalised Wick transform discovered by Thiemann provides a well-established relation between the Euclidean and Lorentzian theories of general relativity. We extend this Thiemann transform to the Ashtekar formulation for gravity coupled with spin-1/2 fermions, a non-Abelian Yang-Mills field, and a scalar field. It is proved that, on functions of the gravitational and matter phase space variables, the Thiemann transform is equivalent to the composition of an inverse Wick rotation and a constant complex scale transformation of all fields. This result holds as well for functions that depend on the shift vector, the lapse function, and the Lagrange multipliers of the Yang-Mills and gravitational Gauss constraints, provided that the Wick rotation is implemented by means of an analytic continuation of the lapse. In this way, the Thiemann transform is furnished with a geometric interpretation. Finally, we confirm the expectation that the generator of the Thiemann transform can be determined just from the spin of the fields and give a simple explanation for this fact.Comment: LaTeX 2.09, 14 pages, no figure

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure

Modified Gravity via Spontaneous Symmetry Breaking

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm for a suitable choice of a parameter) and show the absence of the discontinuity.Comment: 5 pages; revised versio

Astrophysical Bounds on Planck Suppressed Lorentz Violation

This article reviews many of the observational constraints on Lorentz symmetry violation (LV). We first describe the GZK cutoff and other phenomena that are sensitive to LV. After a brief historical sketch of research on LV, we discuss the effective field theory description of LV and related questions of principle, technical results, and observational constraints. We focus on constraints from high energy astrophysics on mass dimension five operators that contribute to LV electron and photon dispersion relations at order E/M_Planck. We also briefly discuss constraints on renormalizable operators, and review the current and future contraints on LV at order (E/M_Planck)^2.Comment: 30 pages, submitted to Lecture Notes in Physics, Quantum Gravity Phenomenology, eds. G.Amelino-Camelia, J. Kowalski-Glikman (Springer-Verlag

Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?

This letter is a critique of Barbero's constrained Hamiltonian formulation of General Relativity on which current work in Loop Quantum Gravity is based. While we do not dispute the correctness of Barbero's formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekar's complex SU(2) connection, Barbero's real SO(3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barbero's real SO(3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.Comment: 12 pages, no figures, revised in the light of referee's comments, accepted for publication in Classical and Quantum Gravit

Lorentz Violation in Extra Dimensions

In theories with extra dimensions it is well known that the Lorentz invariance of the $D=4+n$-dimensional spacetime is lost due to the compactified nature of the $n$ dimensions leaving invariance only in 4d. In such theories other sources of Lorentz violation may exist associated with the physics that initiated the compactification process at high scales. Here we consider the possibility of capturing some of this physics by analyzing the higher dimensional analog of the model of Colladay and Kostelecky. In that scenario a complete set of Lorentz violating operators arising from spontaneous Lorentz violation, that are not obviously Planck-scale suppressed, are added to the Standard Model action. Here we consider the influence of the analogous set of operators which break Lorentz invariance in 5d within the Universal Extra Dimensions picture. We show that such operators can greatly alter the anticipated Kaluza-Klein(KK) spectra, induce electroweak symmetry breaking at a scale related to the inverse compactification radius, yield sources of parity violation in, e.g., 4d QED/QCD and result in significant violations of KK-parity conservation produced by fermion Yukawa couplings, thus destabilizing the lightest KK particle. LV in 6d is briefly discussed.Comment: 26 pages, 2 figures; additional references and discussio

Phenomenological description of quantum gravity inspired modified classical electrodynamics

We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive relations, which are considered up to second order in the inverse of the energy characterizing the quantum gravity scale. The energy-momentum tensor, Green functions and frequency dependent refraction indices are obtained, leading to departures from standard physics. The effective character of the theory is also emphasized by introducing a frequency cutoff. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime the expected corrections get further suppressed by highly oscillating terms, thus forbiding causality violations to show up in the corresponding observational effects.Comment: 14 pages, to be published in Obregon Festschrift 2006, Gen. Rel. and Gra

Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions

We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.Comment: 47 pages; latex fil

Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio

Critical Behavior of the Supersolid transition in Bose-Hubbard Models

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF--CSS transition is in the three-dimensional XY universality class. The SF--XSS transition exhibits non-trivial new critical behavior, and appears, within a $d=3-\epsilon$ expansion to be driven generically first order by fluctuations. However, within a one--loop calculation directly in $d=2$ a strong coupling fixed point with striking ``non-Bose liquid'' behavior is found. At special isolated multi-critical points of particle-hole symmetry, the system falls into the 3d Ising universality class.Comment: RevTeX, 24 pages, 16 figures. Also available at http://www.cip.physik.tu-muenchen.de/tumphy/d/T34/Mitarbeiter/frey.htm