Coupling of a biquaternionic Dirac field to a bosonic field

Theoretical and Mathematical Physics - We extend the biquaternionic Dirac equation to include interactions with a background bosonic Geld. The obtained biquaternionic Dirac equation yields...     

The eigenvalue field is a splitting field

Let K be an algebraically closed field of arbitrary characteristic and F < K a subfield. If is an irreducible semigroup of matrices such that the spectra of all the elements of are contained in F, then is conjugate to a subsemigroup of M _n (F). Research supported in part by the Ministry of Higher Education, Science, and Technology of Slovenia. Received: 6 April 2006     

High harmonic generation in a two-color field composed of a pump field and a weak subsidiary high frequency field

“Coherent control of high-harmonic generation in a two-color field” has been widely concerned. Using split-operator algorithm, we have calculated the high-harmonic generation for helium ion He+ in a two-color field which is composed of a driving field and a weak subsidiary high frequency field (Is=I0/100, （ω,13ω), …(ω, 120ω)) and found that such a field can produce much higher harmonic intensity, typically increasing the harmonics corresponding to the incident frequency of the subsidiary field. The different effects coming from the different subsidiary fields are calculated and analyzed. It is indicated that one of the important underlying mechanisms is high frequency photon induced radiation.     

Class field theory for a product of curves over a local field

We prove that the kernel of the reciprocity map for a product of curves over a p-adic field with split semi-stable reduction is divisible. We also consider the K ₁ of a product of curves over a number field.      

The free fermion field as a Markov field

A definition of a Markov field is given which allows for noncommuting fields. In the commutative case, we recover Nelson's definition (E. Nelson, Construction of quantum fields from Markoff fields, J. Functional Analysis12 (1973), 97–112). Conditional expectations are shown to exist in a regular probability gage space, and, using an independence property of these in the free fermion gage space, it is shown that the free fermion field over $\text{H}$^?1($\text{R}$^d) is a Markov field.     

Resonance effects in the field of a stationary electromagnetic wave and a constant magnetic field

We analyze the interaction of a charged relativistic particle with the electromagnetic field given by a superposition of a stationary wave and a constant magnetic field. The refraction coefficient of the medium is taken different from one. We investigate the problem in the low-signal approximation. To test the results, we used computer simulation of the original system with two scales of the variation rate of the variables taken into account.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 64–71, January, 2005.     

Electromagnetic field in a neighborhood of a focus

The hf wave field near a focus in an inhomogeneous medium is described by a recurrent system of equations the solutions of which are matched with various incoming and corresponding outgoing waves. In particular, a homocentric diaphragm ray solution is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 126–136, 1976.     

Normal approximation of a functional of a Gaussian field

The asymptotic normality of a functional of a strongly correlated Gaussian random field having the meaning of the random volume of a bounded realization of the field over a parallelepiped or triangle is established in this paper. In addition some problems of geometric probabilities are solved: the distribution density of the distance between independent random vectors having uniform distribution in a rectangle or triangle is found.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 55–60, 1988.