Schedule

Domenico Giulini (Leibniz University of Hannover, Hannover, Germany):

Space-Time Symmetries and Energy-Momentum Tensors

In my talk I show how proper geometric formulations of symmetries and energy-momentum tensors eliminate conceptual uncertainties regarding globally conserved quantities and other integral relations, which usually are given in coordinate-dependent language that not only hide their geometric meaning, but also the hypotheses on which they implicitly rest.

Robin Tucker (Lancaster University, Lancaster, Great Britain):

On Gravitational Chirality as the Genesis of Astrophysical Jets

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. I will discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

Alberto Favaro (Imperial College London, London, Great Britain):

The singular geometry of electromagnetic wave propagation

Premetric electrodynamics has provided clarity to different aspects of Maxwell’s theory, e.g. the study of vacuum birefringence, and the controversy on the definition of the energy-momentum tensor (Abraham vs. Minkowski). I will explain how the premetric formulation also brings order to research on anisotropic materials.

Daniel Siemssen (University of Warsaw, Warsaw, Poland):

Quantization of Pre-Metric Electrodynamics and Quantum Inequalities

This talk concerns the quantization of the vector potential in pre-metric electrodynamics with a linear and local constitutive law. If the Fresnel polynomial associated to a constitutive law is hyperbolic, it gives rise to a causality structure which generalizes that of Lorentzian geometry. After a gauge fixing it  is then in many cases possible to construct the retarded and advanced Green’s functions. Their existence forms the basis of the algebraic quantization of the vector potential, as they appear in the commutation relations. In some cases even a ‘vacuum’ state can be found, thus leading to a full quantization. It is known on general grounds that in quantum field theory the pointwise energy density is unbounded from below. Suitably averaged over a region of spacetime or along a ‘timelike’ curve, the energy density can often be shown to be bounded below. This is a so-called quantum energy inequality (QEI). Thanks to the richer causality structure in pre-metric electrodynamics, also more possibilities for different QEIs arise. I will explain general results on QEIs for the pre-metric vector potential, as well as concrete calculations for uniaxial crystals.

Yakov Itin (Hebrew University, Jerusalem, Israel):

Premetric gravity with a local and linear constitutive law

In the standard formulation of general relativity (GR), the metric tensor serves as a primary field variable. This construction is in contrast to gauge theory in which a separation between the premetric field equations and a metric dependent constitutive relation is possible. In this talk, we demonstrate that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.

Wei-Tou Ni (National Tsing Hua University, Hsinchu, Taiwan):

Equivalence principles and Pre-Metric Formalisms

Pre-metric formalisms are general frameworks to test Einstein Equivalence Principle which is the basis of Metric (Pseudo-Riemannian) Geometry in the physical world. Galileo weak equivalence principle is a cornerstone of fundamental physics. We formulate Weak Equivalence Principles WEP I and WEP II for photons in the spirit of Galileo to explore the early universe and quantum gravity. Employing a 4-dimensional pre-metric formulation of electrodynamics of continuous medium and the validity of WEP I for photons (nonbirefringence), the spacetime structure must consist of a core metric field together with an axion field and a dilaton field. Since WEP I for photons is verified empirically to ultrahigh precision, the existence of core metric has been verified to second order in the ratio of Higgs mass to Planck mass. The extension of pre-metric framework to include skewons is formulated by Hehl and Obukhov. The extension of pre-metric framework to gravity part will be reported by Itin, Hehl and Obukhov. I will mention an extension to hyperspace unified theory. I dedicate this talk to Fred Hehl on his 80th birthday.

Dmitri Vassiliev (University College London, London, Great Britain):

Gauge theory from an analyst's perspective

We work with a pair of complex-valued scalar fields over a 4-manifold. Our object of study is a first order Hermitian sesquilinear form, i.e. an integral over the manifold whose integrand is a linear combination of terms "product of gradient of scalar field and scalar field" and "product of two scalar fields". We call two sesquilinear forms equivalent if one is obtained from the other by some $x$-dependent $\mathrm{GL}(2,\mathbb{C})$ transformation, i.e. by a change of basis in the infinite-dimensional vector space of pairs of complex-valued scalar fields. Our aim is to provide an explicit description of equivalence classes of sesquilinear forms. We achieve this aim, and in doing this we show that our sesquilinear forms implicitly contain geometric constructs such as Lorentzian metric, spin structure, connection coefficients and electromagnetic covector potential.

The talk is based on DOI:10.1088/1751-8113/48/16/165203 and arXiv:1611.08297.

Jens Boos (University of Alberta, Alberta, Canada):

Curvature tensors in 4D Riemann-Cartan space

We present the irreducible decomposition of the curvature tensor in a spacetime with curvature and torsion, and discuss the corresponding notions of superenergy in form of a generalized Bel-Robinson tensor.