A one-dimensional invariance principle for gauge fields of integer spin

A relativistic two-particle system is analyzed in which the particles are bound by an harmonic oscillator potential. The system is invariant under τ-reparametrizations as well as under two gauge transformations of the coordinates. The corresponding first-class constraints give a BRST charge which can be used to construct a classical field theory action for all integer spin gauge fields.     

A note on Eisenstein's irreducibility criterion for two-dimensional sampled objects

A proof of uniqueness of phase retrieval for a certain class of objects is given, based on Eisenstein's irreducibility criterion. Some consequences are discussed.     

A plane symmetric solution of Einstein's field equations of general relativity containing zero-rest-mass scalar fields

An exact static solution of Einstein's field equations of general relativity in the presence of zero-rest-mass scalar fields has been obtained when both the metric tensor gijand the zero-rest-mass scalar field φexhibit plane symmetry in the sense of Taub [9]. Our solution generalizes the empty space-time solution with plane symmetry previously obtained by Taub to the situation when static zero-rest-mass scalar fields are present. The static plane symmetric solutoins of Einstein's field equations in the presence of massive scalar fields, and the difference between the massless and non-massless scalar fields are being investigated, and will be published separately later on. We also hope to discuss non-static plane symmetric solutions of Einstein's field equations in the presence of scalar fields in future.     

A note on supersymmetry and magnetic fields

Conclusion In the present article we have considered two supersymmetric non-abelian gauge theories in the presence of an external magnetic field. In has been shown that the effect of the magnetic field breaks suppersymmetry at the one-loop level; however, if supersymmetry is already broken spontaneously at the tree level, then the magnetic field effect does not restore it at the one-loop level. These facts could be used in SUSY GUT models (which are used to describe the early universe), to study phase transition in those models.     

A note on self-dual gravitational fields

In this note we give two new simple derivations of the good-cut equation, the equation which governs (complex) self-dual asymptotically flat gravitational fields. One of these derivations is remarkably simple, involving only a few lines. Our main point of interest, however, is in the second derivation. Though it is slightly more complicated, this method of derivation is almost certainly generalizable to cover real asymptotically flat space-times and thus lead to a generalization of the good-cut equation.     

A note on the impurity spin magnetisation of dilute alloys

Double time temperature dependent anticommutator Green's function has been used to obtain magnetisation of the impurity spin in s-band host metals. The function φ_Ji which is related to the impurity spin magnetisation shows a break in the magnetisation vs temperature curve when $\text{|(}\text{H}{}_0\text{J}\text{) × (}\text{g}{}_{\mathrm{i}}\text{S}{}_{\mathrm{e}}\text{(S}{}_{\mathrm{e}}\text{+ 1))|}$ lies within 1.50. The effect of crystal field of the host lattice on the impurity spin magnetisation has also been considered.     

关于两种二维场类比计算的一点注记

指出《大学物理》1997年第6期上“一类二维时变磁场激发涡旋电场的静电场类比计算”中结果的一点不足之处,并进行了有益的补充。     

A brief note on “extension, spin and non-commutativity”

We show that Dirac’s theory of the electron corresponds to recent approaches based on a non-commutative spacetime.     

Higher spin fields and gravity

We analyze the coupling to gravity of massless bosonic gauge fields of any spin starting from a free theory formulated in terms of a nilpotent BRST operator.     

A note on the existence of phase transitions in finite-site Peierls-Hubbard systems

We discuss spectral properties of a generalizedN-siten-electron Peierls-Hubbard system and examine the possibility of phase transitions of the ground state. ForN=2, it is proved that no phase transition exists. ForN>2, the only possibility of a phase transition is a crossing of two discrete energy levels corresponding to different symmetries.     

A note on the theory of spin wave resonance in spiral structures

The appearance of two resonant modes of spin waves with different non-zero wave vectors is theoretically predicted for a magnetic arrangement of the type of an antiferromagnetic spiral combined with weak antiferromagnetism in the direction of the spiral axis. A study is made of the question of the Hamiltonian suitable for possible applications of the chosen magnetic arrangement, and the possibility of energetic stability of the considered magnetic structure for two concrete realistic forms of the Hamiltonian is pointed out.The author expresses his sincere thanks for valuable discussions and stimulating comments to Dr. S. Krupika and Dr. J. Loos, P. Novák and I. Veltruský of the Institute of Solid State Physics of the Czechoslovak Academy of Sciences, and to Assoc. Prof. J. Morkowski and Assoc. Prof. L. Kowalewski of the Polish Academy of Sciences and Poznan University.     

The existence of scalar Lie fields

It is shown that the existence of nontrivial scalar Lie fields (i. e. fields whose commutator is linear in the field itself) is not precluded by algebraic consistency arguments. A partial characterization of the simplest algebraic Lie field structures is given. Several examples are presented, one of which may be represented by Hermitian operators in a Hilbert space having a unitary representation of the Poincaré group.     

Role of electron spin in integer quantum hall photoluminescence

We investigate numerically the photoluminescence (PL) spectrum in the integer quantum Hall regime and find that the electron spins play important roles. The spectra for the left circularly polarized light show peak splittings when the Fermi levels lies in the excited Landau level, which is caused by the inter Landau level scattering between electrons with anti-parallel spins. At around ν_e∼1 the PL energy is strongly affected by the interplay between the screening and multiple spin flipping (skyrmion) effects.     

A note on the Monte Carlo simulation of one dimensional quantum spin systems

The one dimensional Ising model in a transverse field is treated by Monte Carlo methods in order to study the approach originally proposed by Suzuki, Miyashita and Kuroda.     

Higher spin fields and the Gelfand-Dickey algebra

We show that in 2-dimensional field theory, higher spin algebras are contained in the algebra of formal pseudodifferential operators introduced by Gelfand and Dickey to describe integrable nonlinear differential equations in Lax form. The spin 2 and 3 algebras are discussed in detail and the generalization to all higher spins is outlined. This provides a conformal field theory approach to the representation theory of Gelfand—Dickey algebras.Supported in part by the NSF Grant PHY-84-04931     

Frame-dragging fields and spin 1 gravitomagnetic radiation

Experimental results published in 2004 (Ciufolini and Pavlis in Nature 431:958–960, 2004) and 2011 (Everitt et al. in Phys Rev Lett 106:221101, 1–5, 2011) have confirmed the frame-dragging phenomenon for a spinning earth predicted by Einstein’s field equations. Since this is observed as a precession caused by the gravitomagnetic (GM) field of the rotating body, these experiments may be viewed as measurements of a GM field. The effect is encapsulated in the classic steady state solution for the vector potential field $\zeta $ of a spinning sphere–a solution applying to a sphere with angular momentum J and describing a field filling space for all time (Weinberg in Gravitation and Cosmology, Wiley, New York, 1972). In a laboratory setting one may visualise the case of a sphere at rest $(\zeta =0, \text{ t}<0)$ , being spun up by an external torque at $\text{ t}=0$ to the angular momentum J: the $\zeta $ field of the textbook solution cannot establish itself instantaneously over all space at $\text{ t}=0$ , but must propagate with the velocity c, implying the existence of a travelling GM wave field yielding the textbook $\zeta $ field for large enough t (Tolstoy in Int J Theor Phys 40(5):1021–1031, 2001). The linearized GM field equations of the post-Newtonian approximation being isomorphic with Maxwell’s equations (Braginsky et al. in Phys Rev D 15(6):2047–2060, 1977), such GM waves are dipole waves of spin 1. It is well known that in purely gravitating systems conservation of angular momentum forbids the existence of dipole radiation (Misner et al. in Gravitation, Freeman & Co., New York, 1997); but this rule does not prohibit the insertion of angular momentum into the system from an external source–e.g., by applying a torque to our laboratory sphere.     

A note on the pseudo-fermion representation of a spin 1/2 or 1

Using Abrikosovs pseudo-fermion representation of a single spinS with pseudofermion energy λ=0 we describe a procedure, which allows calculation of thermal statistical averages using standard methods, including the linked cluster theorem of diagrammatic perturbation theory, for the casesS=1/2 andS=1. In particular we derive a relation relevant to the conduction electron Green's function in the Kondo-problem of dilute magnetic alloys.