Ghost neutrinos as test fields in curved space-time

Without restricting to empty space-times, it is shown that ghost neutrinos (their energy-momentum tensor vanishes) can only be found in algebraically special space-times with a neutrino flux vector parallel to one of the principal null vectors of the conformal tensor. The optical properties are studied. There are no ghost neutrinos in the Kerr-Newman and in spherically symmetric space-times. The example of a non-vacuum gravitational pp-wave accompagnied by a ghost neutrino pp-wave is discussed.     

Transport properties of degenerate neutrinos and photons

Transport coefficients are presented for a mixture of neutrinos and nuclei, and for a photon-electron system. The expression are valid for arbitrary degeneracy of the massless component, and include generalizations of Weinberg's results for radiative heat conduction and viscosity.     

Coherent production of photons by neutrinos

The reaction ν+N→ν+N+γ, involving the coherent emission of a photon in a neutrino-nucleus collision, can produce “single shower” events that simulate the reaction ν+e→ν+e. The ratio of coherent photons to electrons (for an ²⁷Al target) is estimated to be 40% at E_ν=20GeV and 10% at E_ν=20 GeV. We examine the extent to which the “excess” of showers seen in the Aachen-Padova experiment could be understood by this mechanism.     

Equivalent charge of photons and neutrinos in a plasma

It is suggested that it is possible to define an equivalent electric charge for an intense laser pulse (which can be described as a photon bunch) propagating in a plasma. It is also shown that this equivalent charge can be a source of new radiation processes in an inhomogeneous plasma. The results are extended to the case of a neutrino bunch, which is coupled to the plasma by weak nuclear forces.     

Definition of the vacuum in curved space-time

It is proposed that the vacuum state of quantized fields in curved space-time be defined as the state which minimizes the average value of the field Hamiltonian. Starting from this definition, equations are obtained for finding positive- and negative-frequency functions for spinor and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–21, July, 1979.     

Conservation theorems in curved space-time

Basic theorems on conservation laws in general space-time are given. The proofs are based on Gauss' theorem which works with ordinary divergence and not with covariant divergence. Consequences for the gravitational theory are exhibited.     

Quantum mechanics in curved space-time

In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild like metric. As a test, the hydrogen atom spectrum is calculated. A comparison of the calculated spectrum with the numerical data of the deuterium energy levels shows a significant improvement of the accord, and the deviations are almost five times smaller then the ones obtained with the Dirac theory. The implications of the theory considering the strong interactions are also discussed.Received: 27 January 2005, Revised: 15 April 2005, Published online: 31 May 2005     

Hadamard renormalization in curved space-time

We derive the family of all Hadamard symmetric kernels for a quantum massive scalar field propagating at a classical curved background, which can be constructed in terms of purely local geometric quantities. No such kernal exists in the massless limit, unless “restricted geometric objects”, which only have a meaning at conformally flat metrics, are used in its construction. We discuss the relation of this result with the anomalous trace of the renormalized vacuum expectation value of the energy-momentum tensor in the case of conformal triviality. Trace anomaly is shown to be inevitable, if the renormalization recipe is defined in terms of purely geometric quantities, as a consequence of the inexistence of a geometric generalization encompassing every possible space-time of the well-known conformal-vacuum at Robertson-Walker universes.     

弯曲时空中的热平衡

讨论了弯曲时空的一种特殊情况--稳态时空中的热平衡条件,利用普朗克黑体辐射定律和广义相对论,得出了两系统通过辐射而达到热平衡时坐标温度相等,但固有温度不相等的结论.     

Conformal anomalies in curved space-time

The general form of the conformal anomaly in a dimensionally regularized theory of massless fermions in a background metric is shown to be determined by the first few terms of weak field perturbation theory.     

Sine-Gordon equation in curved space-time

We study the static solution of the sine-Gordon wave equation in a background geometry determined by a point mass in 1+1 dimension.     

On a Riemannian method in quantum theory about curved space-time

We start from a given Lorentz metric and a vector field of world lines along which observers and measure devices may move. We describe a procedure to associate one-particle Hilbert spaces and one-particle Hamiltonians to space-like hypersurfaces using a transition to a Riemannian metric. With the aid of suitable boundary conditions one can confine the particle within a world tube (box quantization about curved space-time manifolds).Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.     

Velocity of sound in curved space-time

The small-perturbation method of E. M. Lifshits is used to derive expressions for the phase and group velocities of sound in matter described by the equation of state ε=3p in the curved 4-space of Fridman's cosmological model. It is inferred that the curvature of 4-space significantly influences the velocity of sound. Thus, the maximum value of the group velocity of sound in the given model exceeds the maximum value of the velocity of sound in flat 4-space for the same equation of state of matter; for matter of infinite density the velocity of sound is equal to zero at the initial instant of expansion of the universe. These results indicate that when the condition v_so ≤c is taken as the criterion for the choice of equation of state of superdense matter, as for example in relativistic astrophysics, it is necessary to take into account the influence of the curvature of 4-space on the velocity of sound.     

TeV neutrinos and GeV photons from shock breakout in supernovae

We show that as a Type II supernova shock breaks out of its progenitor star, it becomes collisionless and may accelerate protons to energies >10 TeV. Inelastic nuclear collisions of these protons produce an approximately 1 h long flash of TeV neutrinos and 10 GeV photons, about 10 h after the thermal (10 MeV) neutrino burst from the cooling neutron star. A Galactic supernova in a red supergiant star would produce a photon and neutrino flux of approximately 10(-4) erg cm(-2) s(-1). A km(2) neutrino detector will detect approximately 100 muons, thus allowing to constrain both supernova models and neutrino properties.     

Dual charged solution in curved space-time

A dual charged solution carrying both electric and magnetic charge is formulated in SU(2) × U(1) gauge theory without making use of the topological characteristics of Higgs fields. When Dirac quantisation condition is imposed, two consequences follow: (i) Weinberg angle is restricted to the value sin² θ = 1/2 and (ii) the solution cannot have fractional electric change, but must have integer items the basic electric charge of the theory. The infinity inherent in the theory is removed at the classical level by the use of gravitational effects by obtaining the same solution in the curved space-time. The resultant metric is of Reissner-Nordström form.