Gravitational actions in two dimensions and the Mabuchi functional

The Mabuchi energy is an interesting geometric functional on the space of Kähler metrics that plays a crucial rôle in the study of the geometry of Kähler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

The evaluation map in field theory,sigma-models and strings—II

In this paper, we examine specifically the rôle of the evaluation map in sigma-models and strings. We discuss the difference between sigma-models and field theory, as far as anomaly cancellation is concerned. The introduction of the Wess—Zumino terms in different sigma-models is considered. Anomalies in string theory are discussed, with special attention to the conformal anomalies and to the sigma-model anomalies for the imbedded (or immersed) world-sheet of the string. Conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies. In order to have the cancellation of the sigma-model anomalies of the string, certain topological conditions must be satisfied by the ambient manifold. The rôle of the evaluation map in the calculations of global anomalies is also discussed, both for field theories and for sigma-models. In particular global anomalies are connected with the differential characters of Cheeger and Simons. We show that the absence of global anomalies in sigma-models is guaranteed by the absence of torsion in suitable homology groups of the target space.On leave of absence from Dipartimento di Fisica dell'Università di Padova and Instituto Nazionale di Fisica Nucleare, Sezione di PadovaWork supported in part by: Ministero Pubblica Istruzione (research project on Geometry and Physics)On leave of absence from Department of Mathematics, University of North Carolina, Chapel Hill, N.C. 27514. From August 1 until December 20 at the School of Mathematics, Institute for Advanced Study Princeton NJ 08540, USA. Work supported in part by N.S.F.     

Supersymmetry and the Möbius inversion function

We show that the Möbius inversion function of number theory can be interpreted as the operator (–1) ^F in quantum field theory. Consequently, we are able to provide physical interpretations for various properties of the Möbius inversion function. These include a physical understanding of the Möbius Inversion Formula and of a result that is equivalent to the prime number theorem. Supersymmetry and the Witten index play a central rôle in these constructions.     

Twisted invariances of noncommutative gauge theories

We study noncommutative deformations of Yang–Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge transformations. The possible physical rôle of these start-twisted invariances is discussed.     

Some measurements of the spatial coherence of a giant pulse laser

A simple Young-type two-point correlation experiment with photographic detection is described. Comparisons are made for the various factors contributing to the spatial coherence. The determining rôle of the number of superimposed transverse modes is confirmed. The importance of the back mirror, the active medium and the short build-up time is found, experimentally.     

Tunnelling from black holes and tunnelling into white holes

Hawking radiation is nowadays being understood as tunnelling through black hole horizons. Here, the extension of the Hamilton–Jacobi approach to tunnelling for non-rotating and rotating black holes in different non-singular coordinate systems not only confirms this quantum emission from black holes but also reveals the new phenomenon of absorption into white holes by quantum mechanical tunnelling. The rôle of a boundary condition of total absorption or emission is also clarified.     

Determinism,realism, and Stapp's 1985 proof of nonlocality

Two recent criticisms of Stapp's 1985 proof of an incompatibility between locality and quantum mechanics are clarified. One of these criticisms (charging that the proof requires determinism) is supported by a detailed logical analysis of the locality conditions in the proof. The other criticism (charging that the proof assumes realism) is shown to be based upon a misinterpretation of the rôle of counterfactuals in the proof. Further, Stapp's own replies to these criticisms are shown to be inadequate.     

Homogeneous variational complexes and bicomplexes

We present a family of complexes playing the same rôle, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these complexes (apart from the first one) is globally exact. All the complexes may be embedded in bicomplexes, and we show that, again modulo pullbacks, the latter are locally exact. The edge sequence is an important part of such a bicomplex, and may be used for the study of homogeneous variational problems.     

Relativistic fluid dynamics in a non-vacuum régime

The author obtains the fundamental aspects of relativistic fluid dynamics in a non-vacuum régime. As the basic model is taken the special theory of relativity in the form proposed by Einstein (1907), Fock (1955) and others. The model takes account of the influence of the gravitational field upon the velocity of the propagation of light.The research was sponsored by the Research Department, Michigan State University, under the directorship of Mr. John Hoffman, and this is gratefully acknowledged.     

Space–time dimensionality from brane collisions

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes and anti-branes, one of which could play the rôle of our universe. This process also leads to the production of one-dimensional branes and anti-branes, however their number is expected to be suppressed. Brane collisions may also lead to the formation of bound states of branes. Their existence does not alter this result, it just allows for the existence of one-dimensional branes captured within the three-dimensional ones.     

The influence of phonons on quantum diffusion in superconductors

The hopping motion of charged light particles coupled to superconducting electrons as well as to phonons is investigated within the framework of a two-state model. Sufficiently far below the transition temperatureT _c the hopping rate is dominated by one-phonon processes if the static energy shifts between the particle ground states are finite but smaller than twice the BCS energy gap. In the opposite limit of large energy asymmetries phonon coupling does not crucially influence the jump rates. The rôle of nonlinear lattice coupling is investigated.     

The entropy bound and the self-energy of charges in the Schwinger model on black hole backgrounds

We compute the q potential in the Schwinger model on the Schwarzschild black hole. This potential is also discussed using The WKB approximation by considering the rôle of zero modes of massive scalar fields. We study the entropy bound for a charged object using the generalized second law; and at the end, a scenario for charge confinement is proposed on AdS black holes.     

Effet d'aharonov Bohm sur un état borné de l'équation de Schrödinger

Cet article est consacré à l'étude de l'influence du champ magnétique sur la première valeur propre de l'équation de Schrödinger. On se propose d'exploiter quantitativement une remarque d'un article de Lavine O'Carroll par des méthodes semi-classiques. La comparaison de la distance d'Agmon du puits au support du champ magnétique et de la longueur minimale (d'Agmon) des chemins contournant le support joue un rôle essentiel dans les phénomènes mis en évidence.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides, it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field. The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Hamiltoniens àN corps avec champs magnétiques très singuliers du type ‘courte portée’

We study the spectral properties of a large class ofN-body Hamiltonians, in the Agmon formalism, considering magnetic fields with strong singularities and of short-range type. More precisely, we obtain the essential spectrum (a problem that has been solved in a more general setting by Iftimie by a different method), we control the point spectrum embeded in the continuous spectrum, we prove the absence of singularly continuous spectrum and a Limiting Absorption Principle. Our method consists in performing a gauge transformation (obtained by a procedure similar to that used by Boutet-de Monvel-Berthier and Purice that eliminates the magnetic field by adding some perturbation to the electric potential. The perturbation is a first-order differential operator, generally of the long-range type. At this stage we can use the theory without the magnetic field given by Amreinet al.

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Résumé Nous étudions le spectre d'une classe trés générale d'hamiltoniens à N corps dans le formalisme d'Agmon avec des champs magnétiques très singuliers. Il s'agit notamment de calculer le spectre essentiel (probléme deja résolu par Iftimie dans des conditions plus générales, par une autre méthode), de contrôler le spectre ponctuel plongé dans le spectre continu, d'établir l'absence du spectre singulier continu et de prouver un principe d'absorption limite. Par un changement de jauge (dont la construction est basée sur une idée de Boutet de Monvel-Berthier et Purice) on se ramène au cas d'un hamiltonien sans champ magnétique, mais avec les potentiels électriques modifiés, les perturbations étant des opérateurs différentiels du premier ordre, en général du type longue portée. À ce moment là on peut utiliser la théorie sans champ magnétique de Amreinet al.

     

Limits of applicability of Gupta's theory

The applicability of the quantum theory of a weak gravitational field (Gupta's theory) is examined on the basis of the quasiclassical generally relativistic point of view. It is shown that in standard quantum theory the energy of a particle cannot be arbitrary but is bounded both below and above. These bounds arise because it is impossible to treat the region of interaction of elementary particles as a part of flat space. The lower limit depends on the curvature tensor of the external gravitational field, while the upper is determined by the gravitational field of the particle itself.     

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.     

The evaluation map in field theory,sigma-models and strings I

The rôle of the evaluation map in anomaly calculations for field theory, sigma-models and strings is investigated. In this paper, anomalies in field theory (with and without a backgrounds connection), are obtained as pull-backs of suitable forms via evaluation maps. The cohomology of the group of gauge transformations is computed in terms of the cohomology of the base manifold and of the cohomology of the structure group. This allows us to clarify the different topological significance of gauge and gravitational anomalies. The relation between locality and universality is discussed and local cohomology is linked to the cohomology of classifying spaces. The problem of combining the locality requirement and the index theorem approach to anomalies is also examined. Anomaly cancellation in field theories derived from superstrings is analyzed and the relevant geometrical constraints are discussed.On leave of absence from Dipartimento di Fisica dell'Universitá di Padova and Istituto Nazionale di Fisica Nucleare, Sezione di PadovaWork supported in part by: Ministero Pubblica Istruzione (research project on Geometry and Physics)On leave of absence from Department of Mathematics, University of North Carolina, Chapel Hill, N.C. 27514. Work supported in part by N.S.F.