An approach to SU(2) gauge fields in Minkowski space-time

A reparametrization-invariant formulation of SU(2) gauge theory in Minkowski space-time is given in terms of differential forms. A map of space-time into a compact region is used and the SU(2) Maurer-Cartan forms employed to establish a convenient gauge. New solutions to the theory are presented and discussed.     

An application of Morse theory to space-time geometry

Milnor's treatment [6] of Morse's global theory of the calculus of variations for geodesics [7] is restated in the context of space-time geometry: it is seen as providing a link between the curvature and the causal structure of a stably causal globally hyperbolic Lorentzian manifold. An application is discussed.     

Quasiprimary fields: An approach to positivity of 2D conformal quantum field theory

Among the “secondary fields” of Belavin, Polyakov, and Zamolodchikov, the quasiprimary fields are distinguished by their covariant behaviour under infinitesimal Möbius transformations. Local n-point functions can be described in terms of the numerical amplitudes of 3-point functions of quasiprimary fields. The positivity of the full field theory is guaranteed if certain nonlinear consistency conditions among these constants can be satisfied by real numbers. Constraints arising from these conditions are discussed.     

Some remarks on the dynamical origin of charge and space-time quantisation

It is argued here that the concept of dynamical origin of charge as formulated in a previous paper requires the quantisation of space-time. Indeed, in this scheme, it is pointed out that the quantisation of electric charge in unit ofe is a direct consequence of this space-time quantisation.     

Twistors and geometric quantisation theory

The basic geometry of twistors is developed as an application of geometric quantisation theory to the conformal group. It is found, however, that the Kähler form is not positive and that the quantised Hilbert space is trivial. This serves both to highlight difficulties in the quantisation theory for semi-simple Lie groups and to point out some of the obstacles in the way of developing a rigorous theory of twistors. It also suggests some areas in which the interplay between the two theories may be helpful in clarifying issues.     

Symplectic approach to the theory of quantized fields. I

Our aim in this paper the first one of a series concerned with the problem of field quantization starting from the symplectic structure underlying the classical theory, is to build up the variational theory necessary to all further constructions. The basic notions are the vertical bundle and thestructure 1-form used to define thegeneralized infinitesimal contact transformation which allows us to state and solve the variational problem related to field physics.Giving a system of modulevalued differential forms of different degree on the vertical bundle which solutions are the stationary cross sections is the main result in the paper. In this scheme the Euler-Lagrange classical equations are the expressions induced by such a system of differential forms on any cross section of the vertical bundle. This gives us a complete linearization of the Euler-Lagrange equations and, starting from it, a natural globalization of these equations. Finally, the notion of variational problem invariant by a Lie group is defined in this scheme, Noether's theorem related to such invariant problem is formulated and an intrinsic version of the so-called Noether invariants of classical variational calculus is obtained.This work has been realized in the Seminar of Mathematical Physics, directed by ProfessorJ. Sancho, in the Faculty of Science at the University of Barcelona (Spain).     

A theory of extended quantisation

A new theory of quantisation is presented. After arguments are given indicating that mass-energy in the universe is quantised, this quantisation is mathematically related to the lifespan and maximum size of the universe. Various consequences are then deduced, such as the existence of a minimum force.     

The theory of rest-mass quantisation

The general relativity concept of density-dependent space-curvature and the mass-energy relation of special relativity indicate a rest-mass quantisation rule which makes it possible to account for the interconversion of mass and energy in a simple manner and obtain the known quantum postulates as corollaries, thereby throwing new light on the nature of matter and radiation, the uncertainty principle, and the structure of elementary particles.     

Micro-local approach to the Hadamard condition in quantum field theory on curved space-time

For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space-time we prove the equivalence of (1) the global Hadamard condition, (2) the property that the Feynman propagator is a distinguished parametrix in the sense of Duistermaat and Hörmander, and (3) a new property referred to as the wave front set spectral condition (WFSSC), because it is reminiscent of the spectral condition in axiomatic quantum field theory on Minkowski space. Results in micro-local analysis such as the propagation of singularities theorem and the uniqueness up toC of distinguished parametrices are employed in the proof. We include a review of Kay and Wald's rigorous definition of the global Hadamard condition and the theory of distinguished parametrices, specializing to the case of the Klein-Gordon operator on a globally hyperbolic space-time. As an alternative to a recent computation of the wave front set of a globally Hadamard two-point distribution on a globally hyperbolic curved space-time, given elsewhere by Köhler (to correct an incomplete computation in [32]), we present a version of this computation that does not use a deformation argument such as that used in Fulling, Narcowich and Wald and is independent of the Cauchy evolution argument of Fulling, Sweeny and Wald (both of which are relied upon in Köhler's proof). This leads to a simple micro-local proof of the preservation of Hadamard form under Cauchy evolution (first shown by Fulling, Sweeny and Wald) relying only on the propagation of singularities theorem. In another paper [33], the equivalence theorem is used to prove a conjecture by Kay that a locally Hadamard quasi-free Klein-Gordon state on any globally hyperbolic curved space-time must be globally Hadamard.To my parents     

Null surface quantization and quantum theory of massless fields in asymptotically flat space-time

The quantum theory of massless fields in an asymptotically simple space-time is developed. The Schwinger dynamical principle and the Penrose conformal technique are exploited to derive the commutation relations on proper null surfaces in a curved space-time and on null infinities. The explicit expression for theS matrix in an asymptotically simple space-time is presented. The general expression for a density matrix describing particles created in an external field is also given and its possible applications are discussed briefly.     

Large-deviation approach to space-time chaos

In this Letter, we show that the analysis of Lyapunov-exponent fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a gaussian approximation for the large-deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix D (a dynamical invariant itself) is measured and analyzed in terms of its principal components. The application of this method to three (conservative, as well as dissipative) models allows (i) quantifying the strength of the effective interactions among the different degrees of freedom, (ii) unveiling microscopic constraints such as those associated to a symplectic structure, and (iii) checking the hyperbolicity of the dynamics.     

Some structural features induced by the space-time metrical fluctuation in the theory of gravitational fields

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg _λκ (x)=g_λκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT _κ ^λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT _κ ^λμ (i.e.,T _κ ^λμ =δ _κ ^λ σ_μ?δ _κ ^μ σ_λ(σ_μ=?σ/?x ^μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT _κ ^λμ .     

Matter fields in the Plebanski-Demianski space-time

We consider the boson (electromagnetic and gravitational) fields and the fermion (electron and neutrino) fields in the Plebanski-Demianski space-time. In the case of the boson field, we observe that the superradiance phenomena occurs, but in the case of the fermion field we find no super-radiance phenomena     

A real-time approach to nonequilibrium quantum field theory of relativistic fields

Summary The basic ingredients of a real-time nonequilibrium quantumfield theoretical approach, based on a generalization of thermofield dynamics, are briefly reviewed. In particular, the possible advantages of its application to relativistic models, as the φ⁴-model for the Higgs field are pointed out. Also the differences between the above approach and others using the Feynman's path integral method are underlined. ?Angelo della Riccia? Fellow.