To Consider the Electromagnetic Field as Fundamental,and the Metric Only as a Subsidiary Field

In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell’s theory in a diffeomorphism invariant and metric-independent way. The electromagnetic field is then given in terms of the excitation and the field strength F = (E,B). Additionally, a local and linear “spacetime relation” is assumed between H and F, namely H ~ κ F, with the constitutive tensor κ. The propagation is studied of electromagnetic wave fronts (surfaces of discontinuity) with a method of Hadamard. We find a generalized Fresnel equation that is quartic in the wave covector of the wave front. We discuss under which conditions the waves propagate along the light cone. Thereby we derive the metric of spacetime, up to a conformal factor, by purely electromagnetic methods.     

Rigorous model of classical spacetime foam

If in the gravity quantization process one changes from the smooth manifold category to a more general category, qualitatively new features can appear. To illustrate this, we construct a geometrically precise but physically naive model of a classical “spacetime foam” and discuss the consequences of the principle of general covariance and the equivalence principle in this more general setting. We also show how Einstein's equations can be defined on this “spacetime foam”.     

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

We formulate a premetric version of classical electrodynamics in terms of the excitation and the field strength F=(E,B). A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday’s law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.     

Geometry and Physics Today

“Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “physical theories of a geometrical character.” Thence, “physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “differential” equations, are also being discussed.     

GR-Friendly Description of Quantum Systems

We present an axiomatic modification of quantum mechanics with a possible worlds semantics capable of predicting essential “nonquantum” features of an observable universe model—the topology and dimensionality of spacetime, the existence, the signature and a specific form of a metric on it, and a set of naturally preferred directions (vistas) in spacetime unrelated to its metric properties.     

Gravitation,Electromagnetism and Cosmological Constant in Purely Affine Gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous (ΛCDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-Λ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-ΛCDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.     

The Universe Accelerated Expansion using Extra-dimensions with Metric Components Found by a New Equivalence Principle

Curved multi-dimensional space-times (5D and higher) are constructed by embedding them in one higher-dimensional flat space. The condition that the embedding coordinates have a separable form, plus the demand of an orthogonal resulting space-time, implies that the curved multi-dimensional space-time has 4D de-Sitter subspaces (for constant extra-dimensions) in which the 3D subspace has an accelerated expansion. A complete determination of the curved multi-dimensional spacetime geometry is obtained provided we impose a new type of “equivalence principle”, meaning that there is a geodesic which from the embedding space has a rectliniar motion. According to this new equivalence principle, we can find the extra-dimensions metric components, each curved multi-dimensional spacetime surface’s equation, the energy-momentum tensors and the extra-dimensions as functions of a scalar field. The generic geodesic in each 5D spacetime are studied: they include solutions where particle’s motion along the extra-dimension is periodic and the 3D expansion factor is inflationary (accelerated expansion). Thus, the 3D subspace has an accelerated expansion.     

<Emphasis Type="Italic">K</Emphasis>-Causality Coincides with Stable Causality

It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K ⁺ coincides with the Seifert’s relation. As a consequence the causal relation “the spacetime is strongly causal and the closure of the causal relation is transitive” stays between stable causality and causal continuity.     

Local Wick Polynomials and Time Ordered Products¶of Quantum Fields in Curved Spacetime

In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and K?hler, and by Brunetti and Fredenhagen, but they did not impose any “locality” or “covariance” condition in their constructions. As a consequence, their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters. In this paper, we construct an “extended Wick polynomial algebra”– large enough to contain the Wick polynomials and their time ordered products – by generalizing a construction of Dütsch and Fredenhagen to curved spacetime. We then define the notion of a local, covariant quantum field, and seek a definition of local Wick polynomials and their time ordered products as local, covariant quantum fields. We introduce a new notion of the scaling behavior of a local, covariant quantum field, and impose scaling requirements on our local Wick polynomials and their time ordered products as well as certain additional requirements – such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric. For a given polynomial order in powers of the field, we prove that these conditions uniquely determine the local Wick polynomials and their time ordered products up to a finite number of parameters. (These parameters correspond to the usual renormalization ambiguities occurring in Minkowski spacetime together with additional parameters corresponding to the coupling of the field to curvature.) We also prove existence of local Wick polynomials. However, the issue of existence of local time ordered products is deferred to a future investigation. Received: 27 March 2001 / Accepted: 6 June 2001     

Forks in the road, on the way to quantum gravity

In seeking to arrive at a theory of “quantum gravity,” one faces several choices among alternative approaches. I list some of these “forks in the road” and offer reasons for taking one alternative over the other. In particular, I advocate the following: the sum-over-histories framework for quantum dynamics over the “observable and state-vector” framework; relative probabilities over absolute ones; spacetime over space as the gravitational “substance” (4 over 3+1); a Lorentzian metric over a Riemannian (“Euclidean”) one; a dynamical topology over an absolute one; degenerate metrics over closed timelike curves to mediate topology change; “unimodular gravity” over the unrestricted functional integral; and taking a discrete underlying structure (the causal set) rather than the differentiable manifold as the basis of the theory. In connection with these choices, I also mention some results from unimodular quantum cosmology, sketch an account of the origin of black hole entropy, summarize an argument that the quantum mechanical measurement scheme breaks down for quantum field theory, and offer a reason why the cosmological constant of the present epoch might have a magnitude of around 10⁻¹²⁰ in natural units. This paper is the text of a talk given at the symposium on Directions in General Relativity held at the University of Maryland, College Park, Maryland, in May 1993 in honor of Dieter Brill and Charles Minser.     

Relativities and Homogeneous Spaces I

Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and isospin group, on the other side, are discussed under the common concept of “relativity.” A relativity is defined by classes G/H of “little” group in a “general” group of operations. Relativities are representable as linear transformations that are considered for five physically relevant examples.Finite Dimensional Relativity Representations     

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω^-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach. Received: 3 March 1994 / Accepted: 2 February 1995     

Quantum statistical monte carlo methods and applications to spin systems

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem⁽¹⁾ thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures. Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985.     

An Assessment of Evans’ Unified Field Theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ ^α and a (metric compatible) Lorentz connection Γ ^{α β} . These two potentials yield the field strengths torsion T ^α and curvature R ^{α β} . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ ^α to be proportional to four extended electromagnetic potentials ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.     

Theory of superfluidity of nuclear matter based on the Fermi-liquid approach

This paper discusses how an electromagnetic field consisting of a superposition of a constant magnetic field and a field of laser type can affect nuclear beta decay. In general it is not assumed that the intensities of the two types of fields are small compared to the characteristic field H _cr*=β ₁ H _cr, where H _cr=m ² c ³/eℏ and the quantity β ₁ depends on the energy liberated in the decay and the configuration of the electromagnetic field. For nonrelativistic decays the quantity β ₁ is found to be of the same order as the maximum kinetic energy of an electron referenced to its rest energy β ₁∼I≪1. It is assumed that the frequency of the wave field satisfies ℏω/mc ²⩽I. The behavior of the probability for the process is studied over a wide range of the fundamental parameters that characterize the fields. Corresponding asymptotic expressions are derived in the “weak”-and “strong”-field regimes. Also discussed are so-called interference corrections to the unperturbed decay probability, which cannot in principle be studied by the methods of perturbation theory. It is shown that the times and distances that are important in generating these contributions exceed the parameters of the unperturbed processes, just as in the case of a plane-wave field previously investigated in detail by Nikishov and Ritus. However, in contrast to the case of a pure wave field, when a system is simultaneously subjected to a constant magnetic field and a wave field, the degree to which these characteristic regions are enlarged can depend not only on the intensities of the electromagnetic fields but also on their rates of change, even in the limit in which the wave field is slowly varying. Zh. éksp. Teor. Fiz. 111, 3–24 (January 1997)     

Quadratic curvature gravity with second order trace and massive gravity models in three dimensions

The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In n > 4 dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is “square root” of the former are presented.     

New organic FET-like photoactive device, experiments and DFT modeling

We present the possible construction of an organic FET-like photoactive device in which source-drain current through a phthalocyanine ( H₂Pc film is affected by a photo-induced dipolar field in a photoactive “gate” electrode. The influence of the dipolar electric field on charge transfer between H₂Pc molecules is modeled by DFT quantum-chemical calculations on H₂Pc dimers and tetramers.     

Dark energy and gravity

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T _ab → T _ab + Λ _gab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.     

Degenerate Solutions of General Relativity from Topological Field Theory

Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional $BF$ theory on any framed surface Σ embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Σ, while inside this neighborhood the connection A and the field satisfy the equations of 4-dimensional BF theory. Our construction works in any signature and with any value of the cosmological constant. If for some 3-manifold S, at fixed time our solutions typically describe “flux tubes of area”: the 3-metric vanishes outside a collection of thickened links embedded in S, while inside these thickened links it is nondegenerate only in the two transverse directions. We comment on the quantization of the theory of solutions of this form and its relation to the loop representation of quantum gravity. Received: 21 April 1997 / Accepted: 22 August 1997