Twistor diagram equalities for generalized mass-scattering integrals for Dirac fields

A method which enables one to convert the integral of a holomorphic projective twistor one-form into the integral of a holomorphic projective twistor three-form is used to modify the end-vertex structures of certain twistor diagrams that represent mass-scattering integrals for Dirac fields. Each term of the twistorial diagrammatic expansions recovering the entire fields is then re-expressed appropriately. This gives rise to four sets of explicit twistor-diagram equalities for the mass-scattering formulae.I am most grateful to Professor Roger Penrose for making a key point concerning the introduction of the basic auxiliary-twistor vertices. My warmest thanks go to the World Laboratory for supporting this work financially. I wish to acknowledge the Third World Academy of Sciences for a relevant travel grant. I am grateful, also, to Dr. Asghar Quadir for his invaluable suggestions.     

Anisotropic transport of charge and complexified duality

Charge transport in two dimensions provides an ideal laboratory for investigating parameter space geometries. The Onsager relations for anisotropic transport in a parity-violating external field endow these spaces with a highly nontrivial complex (and Kähler) structure, which can be given a simple geometrical interpretation. A large class of Coulomb gases exhibiting this structure have a generalized Kramers-Wannier symmetry (complexfield duality) which is contained in the modular group. Knowledge of this symmetry and the degrees of freedom encoded in the Coulomb gas appear to be sufficient to determine the global phase diagram and the renormalization group fixed-point structure, including the critical exponents. This accounts for all the scaling behavior observed so far in the quantum Hall system.     

Massive ghost Dirac fields in Einstein-Cartan theory

An exact solution of the Einstein-Cartan-Dirac equations with cosmological constant and vanishing energy-momentum tensor is presented.     

Quantum field theory of Dirac monopoles and the charge quantization condition

A relativistic quantum field theory of Dirac monopoles in interaction with electric charges is presented. A path-integral quantization is used to discuss the renormalization and derive the Dirac charge quantization condition after higher order effects have been included.     

Dirac particle in the presence of a plane waveand constant magnetic fields: path integral approach

The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of a path integral via the Alexandrou et al. formalism according to the so-called global projection. As a calculation tool, we introduce two identities (constraints) into this formalism; their main role is the reduction of the dimension of the integral and the emergence in a natural way of some classical paths and, due to the existence of a constant electromagnetic field, we have used the technique of fluctuations. Hence the calculation of the GF is reduced to a known Gaussian integral plus a contribution from the effective classical action.Received: 22 January 2005, Revised: 16 May 2005, Published online: 9 August 2005     

A twistorial description of the dynamics of complexified dirac fields

A method that allows the construction of a twistorial least-action principle for complexified Klein-Gordon fields is adapted to the context of the two-component theory of Dirac fields. It appears that the viability of the adaptation procedures rests crucially upon the freedom in the selection of spinor kernels for the integrands of the universal twistor contour integrals for massive fields carrying arbitrary spin. An intrinsic ambiguity borne by the inner structure of the twistor representation of the dynamics of the spinning fields taken into consideration is then brought out. This feature appears to be reflected by the fact that many Poincaré-invariant Lagrangian densities can be regarded as candidates for entering the new variational principle. It is remarked that all the corresponding equations of motion agree with a single twistor translation of the pertinent field equations. The dynamical expressions that result from the implementation of the procedures turn out to be related to one another through a simple interchange scheme. A set of wave equations for the system allowed for is also obtained. This work was supported financially by the Brazilian agency CNPq.     

Path integral for one-dimensional Dirac oscillator

In this paper we derive the propagator for the one-dimensional Dirac oscillator using the supersymmetric path integral formalism. The spin calculations are carried out with the help of the technique of Grassmann functional integration. The Green function is exactly evaluated. The Polyakov spin factor is explicitly derived and the energy spectrum and the corresponding wave functions are deduced. PACS 03.65.Ca; 03.65.Db; 03.65.Ge; 03.65.Pm     

Canonical variables for the Dirac theory

A new canonical structure for Dirac's theory is proposed. The new configuration space A is a real, four-dimensional subbundle of the spinor bundle. A Lagrangian defined on Q describes a theory equivalent to the Dirac one. In this way we obtain a theory without second-type constraints.     

The development of ideas in twistor theory

This paper presents a review of the main concepts of twistor theory. The emphasis is on the evolution of the subject from the original motivating ideas to the more recent work. In particular the physical and philosophical reasoning behind the use of the various mathematical structures is discussed.     

Green's function of a generalized Dirac equation for constant fields

Schwinger's method is used to find the Green's function for a Dirac equation in which the presence of anomalous moments of the fermion is taken into account phenomenologically and constant and homogeneous electromagnetic fields are assumed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 70–75, November, 1980.     

Path integral for a Dirac particle in a quantized plane wave field

The problem of a relativistic spinning particle interacting with a quantized electromagnetic plane wave is treated by employing path integral methods and introducing the notion of a coherent state action. The dynamics of the particle spin is described using the supersymmetric action proposed recently by Alexandrou et al. in the so-called global representation. It is shown that to obtain the relative causal Green function, two fermionic identities, related directly to the classical equations of motion, have to be incorporated. The Green function, as constructed, allows us to extract in a natural way the expressions of the corresponding energy spectrum and wave functions. Received: 26 July 2002 / Revised version: 11 September 2002 / Published online: 25 October 2002     

Tau functions and the twistor theory of integrable systems

We first define τ-functions as generalized cross-ratios of four points on a finite- or infinite-dimensional Grassmannian. We show how this definition can be used to construct a natural flat connection on a determinant line bundle associated with two equivariant holomorphic vector bundles over a twistor space, provided that the action of the symmetries on the bundles has the same normal form at the fixed points for the two bundles. The determinant line bundle has a natural meromorphic section of which the logarithmic covariant derivative is the logarithmic derivative of the τ-function. We establish a natural product formula for this τ-function; we show that it vanishes at the jumping lines of one bundle and has poles at the jumping lines of the other. We also show that this definition leads to standard expressions for the τ-functions of the KdV equation, the Ernst equation, and the isomonodromic deformation equations. We describe a new twistor treatment of the isomonodromic deformation equations.     

Dirac quantization of a supersymmetric field theory

The superfield of one-space dimensional field theory is quantized using Dirac's method of quantization of systems with constraints. The quantization is shown to be consisted with that of the component fields.     

New exact Einstein-Maxwell fields for a massless charge

New solutions of the Einstein-Maxwell equations are presented. The solutions describe the gravitational fields of a massless charge.     

On the adiabatic limit for Dirac particles in external fields

An adiabatic switching formalism is proposed to bypass the difficulties in defining the spontaneous pair creation in static electromagnetic fields.On leave from I.F.I.N. Bucharest, Rumania