Krichever-Novikov global operator formalism: NSR superstring in curved background

The Neveu-Schwarz-Ramond type II closed superstring is considered to evolve in a curved space-time manifold. The Krichever-Novikov global operator formalism is used to construct the generators of a super-conformal algebra on a Riemann surface . The computation for the quantum algebra of these generators is explicitly presented. It is shown that the theory is free from super-conformal anomalies if the target manifold is ten dimensional and satisfies the Ricci flatness condition.     

On the electronic spectrum in curved graphene nanoribbons

Using the formalism of the Dirac equation for curved space-time in the Friedmann model of a non-stationary universe, we calculate the electronic spectrum and density of states in curved graphene nanoribbons. Based on the obtained density of states we further study the current-voltage characteristics of the nanoribbonmetal tunnel junction. The dependence on the geometric characteristics of the nanoribbon has been revealed, showing a great influence of such parameters as the number of carbon atoms and the characteristic frequency of distortion.     

A canonical formulation of dissipative mechanics using complex-valued hamiltonians

We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean hamiltonian operators. The excited states are unstable and decay to the ground state. We also compute the tunneling amplitude across a potential barrier by solving the dissipative version of the Schrödinger equation. We then generalize the formalism to cases where the configuration space is a curved Riemannian manifold.     

Connexions conformes sur un fibré vectoriel

We introduce a new formalism to define conformal connections on a vector bundle, endowed with a conformal class of pseudo-riemannian metrics of signature (p, q). Using a bundle map, called isotropic transformation, we show that these non-linear connections are in one-to-one correspondence with metric connections on an enlarged pseudo-riemannian vector bundle, endowed with a metric of signature (p + 1, q + 1). We then use this formalism to give an intrinsic definition of Cartan's conformal circles. Finally, as an example, we give a geometric interpretation of some results of relativistic electromagnetism, connecting to each electromagnetic field a conformal connection on the tangent bundle of the space-time manifold.     

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Using a strongly covariant formalism given by Carter for the deformations dynamics of p-branes in a curved background and a covariant and gauge invariant geometric structure constructed on the corresponding Witten's phase space, we identify the canonical variables for Dirac–Nambu–Goto (DNG) and Gauss–Bonnet (GB) system in string theory. Future extensions of the present results are outlined.     

Symmetries and motions in manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependent co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an a priori infinite-dimensional Lie algebra. The nature of such infinite algebras is clarified using the example of flat space-time. Next the formalism is extended to spinning space, which in addition to the standard real co-ordinates is parametrised also by Grassmann-valued vector variables. The equations for extremal trajectories (“geodesics”) of these spaces describe the pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve for the motion of a pseudo-classical electron in Schwarzschild space-time.     

On the vanishing of multiloop contributions to the 0-, 1-, 2-, 3-point functions in the Green-Schwarz formalism for the heterotic strings

We analyse the structure of insertions arising in multiloop calculations in the first-quantized version of the Green-Schwarz formalism. We show that at least four constant zero modes of grassmannian ϑ-fields related to space-time supersymmetry are not removed by insertions. The occurrence of these zero modes straightforwardly leads to non-renormalization theorems, which imply that all 0-, 1-, 2-, 3-point functions vanish.     

The Fluctuation Theorem as a Gibbs Property

Common ground to recent studies exploiting relations between dynamical systems and nonequilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti–Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz–Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property, as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics.     

Hamiltonian Dynamics for Einstein’s Action in <Emphasis Type="Italic">G</Emphasis>→0 Limit

The Hamiltonian analysis for the Einstein’s action in G→0 limit is performed. Considering the original configuration space without involve the usual ADM variables we show that the version G→0 for Einstein’s action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis.     

Tachyons in general relativity

The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.     

Higher-spin fields in a curved space-time

Algebraic constraints are derived for higher-spin fields in a curved space-time manifold. Comparison is made with previously obtained results. A particular solution of the zero-restmass field equations is given for the plane wave Einstein-Maxwell space-times.     

The dispersion of gravitational waves

A definition is given of a plane gravitational wave in a curved background space-time manifold. For a particular background metric, a dispersion relation for the waves is derived analogous to that satisfied by plane electromagnetic waves in a dilute plasma.     

A Relativistic Version of the Ghirardi–Rimini–Weber Model

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times.     

弯曲时空几何光学中的聚焦定理

严格、详细地证明了弯曲时空几何光学中的聚焦定理.     

The generalized radiation gauge in curved space-time

In the following we give a necessary and sufficient criterion for the existence of theU(1) radiation gauge in a curved space-time with isometry. This criterion is purely geometric and leads to a (local) 3+1-split of space-time with vanishing extrinsic curvature. If the symmetry is timelike and in absence of charges the generalization of the Coulomb gauge leads to a time evolution of the Maxwell field which is analogous to that in flat space-time.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.