Green function theory of a Heisenberg ferromagnet with dipole-octupole interactions

The effect of dipole-octupole interaction on different magnetic parameters for the spinS=3/2 system in the presence of biquadratic exchange has been investigated. The Green function technique with random phase approximation (RPA) has been employed to obtain analytical results. These results are in good agreement with the results of the molecular field approzimation (MFA).     

Failure of reflection positivity in the quantum Heisenberg ferromagnet

We show that reflection positivity does not hold in the finite-volume spin 1/2 quantum Heisenberg ferromagnet in two cases: (i) for any dimension or degree ofS ¹-invariant anisotropy, above a volume independent temperatureT ₀, and (ii) for the isotropic model in one dimension, below a volume dependent temperatureT ₁.     

First order green-function theory of isotropic Heisenberg ferromagnet

The Heisenberg ferromagnet with general spin S is considered within Green-function theory and spectral density method. New difference equations of the first order determining one- and two-particle correlation functions are derived and solved. The spectral density method is used to close Oguchi's variational theory without additional decoupling assumptions. The temperature renormalized spectrum is found to be a series expansion in that the first term coincide with RPA result and the first two terms correspond essentially to Callen's result. Low temperature expansions for the renormalization factor and the magnetization are given and shown to coincide with Callen's result.     

On a new approach to the theory of the Heisenberg ferromagnet

Summing up the infinite classes of the Feynman diagrams for the spin operators with increasing power of the high density parameter we obtained the formulas both for the magnetization and the free energy. These formulas include the gaussian fluctuations of self-consistent field as well as scattering of spin waves on these fluctuations.     

Four-dimensional BF theory as a topological quantum field theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4,) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds.     

低维量子磁性和量子海森伯反铁磁体之有效场论

文章对低维量子磁性的基本问题和相关研究进展作了简单评述,强调了量子非线性Sigma模型在研究量子海森伯反铁磁体的低能物理方面所起的作用以及理论本身存在的疑难问题,并简单介绍了作者最近提出的克服这些疑难问题的一个新建议.     

低维量子磁性和量子海森伯反铁磁体之有效场论

文章对低维量子磁性的基本问题和相关研究进展作了简单评述，强调了量子非线性Sigma模型在研究量子海森伯反铁磁体的低能物理方面所起的作用以及理论本身存在的疑难问题，并简单介绍了作者最近提出的克服这些疑难问题的一个新建议．     

A Feynman-Kac formula for the quantum Heisenberg ferromagnet. II

This article continues the analysis of the first arcticle under the same title. Using methods of stochastic analysis we prove Feynman-Kac formulas for the relevant heat kernels. We also present classical limit theorems.Dedicated to Res Jost and Arthur Wightman     

A Feynman-Kac formula for the quantum Heisenberg ferromagnet. I

The Hamiltonian of the (anisotropic) quantum Heisenberg (anti-) ferromagnet on an arbitrary finite lattice is lifted to a Hamiltonian acting on sections of the bundle obtained by twisting a certain line bundle over the classical spin configuration space (which is a Kähler manifold) with the Dolbeault complex. This procedure is extended fromSU(2) to arbitrary compact semi-simple Lie groups and arbitrary irreducible representations. The Bott-Borel-Weil theorem gives a heat kernel representation for the original partition function in an external magnetic field. TheU(1)-gauged local Hamiltonian is the sum of the free, supersymmetric, twisted Dolbeault Laplace operator (multiplied by the inverse of an arbitrary small mass parameter) plus the lifted Hamiltonian.The resulting (Euclidean) Lagrangian is nonlocal and describes bosons which do and fermions which do not propagate through the lattice. All fields couple to the external magnetic field. The Lagrangian contains Yukawa and Luttinger type interactions.     

Spiral-logarithmic structures in a Heisenberg ferromagnet

Spiral-logarithmic structure is suggested as a stationary solution of a modified equation for the Heisenberg model, and the single-and N-soliton solutions are constructed on this base.     

Physical realization of topological excitations in quantum Heisenberg ferromagnet on lattice

The physical spin configurations corresponding to the topological excitations expected to be present in the XY limit of a purely quantum spin \frac 12\frac {1}{2} Heisenberg ferromagnet, are investigated on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed by making use of the coherent spin field components from meronic (anti-meronic) configurations in the limiting case of very strong XY anisotropy. The equations for pseudo-time evolution of coherent spin fields used in this analysis, are obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg ferromagnet on lattice. The important role of the associated topological-like term extracted from the Wess-Zumino-like contribution, is highlighted in our procedure. It is shown that this term can identify a large class of vortices (anti-vortices). In particular the excitations having odd topological charges form this class. Our present formalism is markedly different from the conventional approach for the construction of quantum vortices (anti-vortices).     

quantum field theory as group algebra

A group theoretical approach to dynamical quantization in general, and quantum field theory in particular, is developed. This approach opens possibilities of new quantization schemes. Some of these schemes are discussed in detail. They offer certain advantages such as relaxation of the conventional principles of unitarity and causality on the one hand and the possibility to attach some meaning to the formal solutions of the equations of unitarity and causality in terms of functional integrals on the other.     

The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/τ, a and τ being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=ζc and ζ=ζ(m) mass-dependent. For c the speed of light ζ−1 is a vacuum refraction index that increases monotonically from ζ−1(0)=1 to ζ−1(M)=∞, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.     

Structurally disordered Heisenberg ferromagnet

The effect of structural disorder on the properties of a Heisenberg ferromagnet is considered within the Bethe-Peierls-Weiss approximation. It is concluded that the details of the structural disorder, and its effect on the exchange interactions between localized spins, determine the direction of change in the Curie temperature with respect to the crystalline case.     

The Faddeev equations for the Heisenberg ferromagnet

The Faddeev equations for the three-magnon T-matrix of the Heisenberg ferromagnet with nearest neighbour interactions are derived for the cubic lattice in arbitrary dimensions. The extreme case of spin $\text{1}\text{2}$ is considered and the kinematical restriction, that only one spin deviation per site is possible, has been taken into account rigorously. Hence the T-matrix is unitary and suited for the study of bound state as well as scattering state properties. The analytic solution of the homogeneous Faddeev equations in one dimension is given.     

Two-dimensional quantum electrodynamics as a model in the constructive quantum field theory

We investigate a transformation of two-dimensional quantum electrodynamics ((QED)₂)-type models into sine-Gordon models in the constructive method.     

Susceptibility of compressible Heisenberg ferromagnet

The spin-phonon spin $\text{1}\text{2}$ Heisenberg system is found to have the same critical index for the susceptibility as the ideal, rigid lattice ferromagnet. This is in accordance with the criterion for critical index renormalisation expounded by Fisher in terms of the sign of the specific heat index.