Euclidean Fermi fields with a hermitean Feynman-Kac-Nelson formula. I

We construct free, Euclidean, spin one-half, quantum fields with the following properties: (i) CAR; (ii) Symanzik positivity; (iii) Osterwalder-Schrader positivity; (iv) no doubling of particle or spin states. They admit the recovery of the relativistic Dirac field by the Osterwalder-Schrader technique. We then formally parametrize interacting theories by a natural class of Hermitean, Euclidean actions, and obtain a simple, Hermitean, Feynman-Kac-Nelson formula. The interacting theory formally obeys all the properties (i)–(iv), and admits the reconstruction of a physical Hilbert space, including a Hermitean, contraction semigroup for the Wick rotated time evolution. We propose a system of axioms for the interacting theory.     

The Free Will Theorem

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic and causal. We also establish the consistency of our axioms and discuss the philosophical implications.     

The nucleon wave function in light-front dynamics

The general spin structure of the relativistic nucleon wave function in the 3q-model is found. It contains 16 spin components, in contrast to the 8 already known. This follows from the fact that in a many-body system parity conservation does not reduce the number of components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results.     

Ion acceleration regimes in underdense plasmas

Acceleration of large populations of ions up to high (relativistic) energies may represent one of the most important and interesting tools that can be provided by the interaction of petawatt laser pulses with matter. In this paper, the basic mechanisms of ion acceleration by short laser pulses are studied in underdense plasmas. The ion acceleration does not originate directly from the pulse fields, but it is mediated by the electrons in the form of electrostatic fields originating from channeling, double layer formation and Coulomb explosion     

The microcanonical ensemble of the ideal relativistic quantum gas with angular momentum conservation

We derive the microcanonical partition function of the ideal relativistic quantum gas with fixed intrinsic angular momentum as an expansion over fixed multiplicities. We developed a group theoretical approach by generalizing known projection techniques to the Poincaré group. Our calculation is carried out in a quantum field framework and applies to particles with any spin. It extends known results in the literature in that it does not introduce any large volume approximation, and it takes particle spin fully into account. We provide expressions of the microcanonical partition function at fixed multiplicities in the limiting classical case of large volumes and large angular momenta and in the grand-canonical ensemble. We also derive the microcanonical partition function of the ideal relativistic quantum gas with fixed parity.     

Massive higher spin fields coupled to a scalar: Aspects of interaction and causality

We consider in detail the most general cubic Lagrangian which describes an interaction between two identical higher spin fields in a triplet formulation with a scalar field, all fields having the same values of the mass. After performing the gauge fixing procedure we find that for the case of massive fields the gauge invariance does not guarantee the preservation of the correct number of propagating physical degrees of freedom. In order to get the correct number of degrees of freedom for the massive higher spin field one should impose some additional conditions on parameters of the vertex. Further independent constraints are provided by the causality analysis, indicating that the requirement of causality should be imposed in addition to the requirement of gauge invariance in order to have a consistent propagation of massive higher spin fields.     

Charged scalar fields in an external magnetic field: Renormalisation and universal diamagnetism

The physical and mathematical mechanism behind diamagnetism of N (finite) spinless bosons (relativistic or non-relativistic) is well known. The mathematical signature of this diamagnetism follows from Kato's inequality while its physical way of understanding goes back to Van Leeuwen. One can guess that it might be true in the field theoretic case also. While the work on systems with a finite number of degrees of freedom suggests that the same result is true in a field theory, it does not by any means prove it. In the field theoretic context one has to develop a suitable regularisation scheme to renormalise the free energy. We show that charged scalar fields in (2+1) and (3+1) dimensions are always diamagnetic, even in the presence of interactions and at finite temperatures. This generalises earlier work on the diamagnetism of charged spinless bosons to the case of infinite degrees of freedom. We also discuss possible applications of the theory.     

自旋不是轨道角动量的相对论效应——与许方官和高春媛商榷

对《大学物理》2000年第11期上发表的《氢原子的磁矩－对自旋的讨论之一》一提出了不同的看法，认为该错把相对论的流密度当成了非相对论的流密度，前不能在非相对论近似下过滤到后，在相对论情况下，自旋和轨道耦合在一起，不能互相独立，在非相对论情况下自旋独立于轨道运动而存在；因而，自旋不是轨道角动量的相对论效应。     

Relativistic quantum field theory with fractional spin and statistics

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincaré group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.     

Mass spectra of dual strings

Dual strings seem to correspond uniquely to certain subgroups of the modular group. From three axioms, one of which is a tentative simplicity assumption, a finite number of possible mass spectra is derived, but not yet the corresponding amplitudes. Above space-time dimension 8, this approach yields just the mass spectra of the known models, plus one additional candidate for 10 dimensions. Further models exist probably for dimensions 8, 6, and 4, and perhaps for dimensions 5 and 3. The mass spectrum of one candidate for the “correct model” is determined. It yields only mesons of charge zero, but otherwise the agreement with experiment is amazing.     

Consequences of relativity for the hyperfine interactions — with applications to transition metals

The strong influence of relativity on the hyperfine interaction is demonstrated by non-, scalar andfully relativistic calculations for solid transition metal systems. By calculations of hyperfine fields andof the nuclear spin lattice relaxation rate of Ag in Ag _x Pt_1–x it is shown that scalar relativistic calculations, which neglect the influence of spin-orbit coupling, seem to be sufficient to account for relativistic effects in many cases. To account properly for the symmetry-breaking caused by spin-orbit coupling, which is reflected by many hyperfine interaction properties, a fully relativistic approach is demanded. The corresponding formalism in the framework of the KKR-GF (Korringa-Kohn-Rostoker-Green's function) method of band structure calculation for magnetic solids is outlined. As applications results for the hyperfine fields of pure transition metals andalloys are presented.     

Effect of Gd-Mn exchange on phase transitions in GdMn<Subscript>2</Subscript>O<Subscript>5</Subscript> induced by a strong magnetic field

Complex studies of the magnetic, magnetoelectric, and magnetoelastic properties of GdMn₂O₅ single crystals in strong pulsed magnetic fields are carried out in order to obtain additional indirect information on the character of the rare-earth and manganese spin ordering. It is shown that magnetic ordering of Gd³⁺ spins affects the manganese sublattice spin orientation and initiates new magnetic phase transitions. The observed magnetoelectric properties of the GdMn₂O₅ system are interpreted in terms of the theory of phase transitions.     

Isometric motion in relativistic magnetohydrodynamics

The general relativistic barometric formulas of a perfect charged relativistic ther modynamical fluid with constant magnetic permeability and infinite conductivity are deduced if the space-time, in which this fluid is moving, has two Killing vector fields: the first collinear to the 4-velocity with the second one proportional to the magnetic field.     

Spin asymmetry in an intense-field ionization process

A relativistic analysis of the rate of spin flips in ionization of an ensemble of Dirac H atoms subjected to intense circularly polarized laser fields is made. A remarkable intensity-dependent asymmetry between the spin up and spin down electron currents is found. It is nonzero even when the retardation effect, hence the magnetic component of the field, as well as the spin-orbit interaction responsible for the well-known Fano effect, is negligible. Transformation properties of the amplitudes show that the sign of asymmetry can be controlled by changing the helicity of the laser photons from outside.     

Fields on the Poincaré Group: Arbitrary Spin Description and Relativistic Wave Equations

In this paper, starting from a pure group-theoretic point of view, we develop an approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincaré group. Such fields can be considered as generating functions for conventional spin-tensor fields. The case of two, three, and four dimensions are elaborated in detail. Discrete transformations C, P, T are defined for the scalar fields as automorphisms of the Poincaré group. We classify the scalar functions, and obtain relativistic wave equations for particles with definite spin and mass. There exist two different types of scalar functions (which describe the same mass and spin), one related to a finite-dimensional nonunitary representation and the other to an infinite-dimensional unitary representation of the Lorentz subgroup. This allows us to derive both usual finite-component wave equations for spin-tensor fields and positive-energy, infinite-component wave equations.     

Theory and simulation of positionally frozen Heisenberg spin systems

The structure, thermodynamics and the ferromagnetic phase transition of a positionally frozen disordered Heisenberg spin system are studied by means of extensive Monte Carlo calculations in combination with finite size scaling techniques, as well as resorting to the Replica Ornstein-Zernike formalism. The system is formed by a collection of Heisenberg spins whose spatial distribution corresponds to a soft sphere fluid with its particle positions frozen at a certain quench temperature. The spin orientations are allowed to equilibrate at a given equilibrium temperature. If the quench and equilibrium temperatures are similar the properties of the positionally frozen system are practically indistinguishable from those of the fully equilibrated Heisenberg spin fluid. On the other hand, one observes that as the quenching temperature of the spatial degrees of freedom increases, so does the Curie temperature of the Heisenberg spins. The theory fails to reproduce the location of the ferromagnetic transition, despite its relative accuracy in the determination of the orientational structure in the supercritical region.Received: 25 July 2003, Published online: 9 September 2003PACS: 75.50.Lk Spin glasses and other random magnets - 64.60.Fr Equilibrium properties near critical points     

Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances

Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark-gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin-orbit coupling. The key insight is that the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields: the Pauli system can be viewed as Yang-Mills quantum-mechanics in a ‘fixed frame’, and it can be viewed as an ‘analogous system’ for non-Abelian transport in the same spirit as Volovik’s identification of the He superfluids as analogies for quantum fields in curved space time. We take a similar perspective as Jackiw and coworkers in their recent study of non-Abelian hydrodynamics, twisting the interpretation into the ‘fixed frame’ context, to find out what this means for spin transport in condensed matter systems. We present an extension of Jackiw’s scheme: non-Abelian hydrodynamical currents can be factored in a ‘non-coherent’ classical part, and a coherent part requiring macroscopic non-Abelian quantum entanglement. Hereby it becomes particularly manifest that non-Abelian fluid flow is a much richer affair than familiar hydrodynamics, and this permits us to classify the various spin transport phenomena in condensed matter physics in an unifying framework. The “particle based hydrodynamics” of Jackiw et al. is recognized as the high temperature spin transport associated with semiconductor spintronics. In this context the absence of faithful hydrodynamics is well known, but in our formulation it is directly associated with the fact that the covariant conservation of non-Abelian currents turns into a disastrous non-conservation of the incoherent spin currents of the high temperature limit. We analyze the quantum-mechanical single particle currents of relevance to mesoscopic transport with as highlight the Ahronov-Casher effect, where we demonstrate that the intricacies of the non-Abelian transport render this effect to be much more fragile than its abelian analog, the Ahronov-Bohm effect. We subsequently focus on spin flows protected by order parameters. At present there is much interest in multiferroics where non-collinear magnetic order triggers macroscopic electric polarization via the spin-orbit coupling. We identify this to be a peculiarity of coherent non-Abelian hydrodynamics: although there is no net particle transport, the spin entanglement is transported in these magnets and the coherent spin ‘super’ current in turn translates into electric fields with the bonus that due to the requirement of single valuedness of the magnetic order parameter a true hydrodynamics is restored. Finally, ‘fixed-frame’ coherent non-Abelian transport comes to its full glory in spin-orbit coupled ‘spin superfluids’, and we demonstrate a new effect: the trapping of electrical line charge being a fixed frame, non-Abelian analog of the familiar magnetic flux trapping by normal superconductors. The only known physical examples of such spin superfluids are the ³He A- and B-phase where unfortunately the spin-orbit coupling is so weak that it appears impossible to observe these effects.     

Nonexistence of quantum fields associated with two-dimensional spacelike planes

It is shown that in a relativistic quantum field theory satisfying Wightman's axioms, there are no nontrivial field-like operators, or even bilinear forms, associated to a two (or less)-dimensional spacelike plane in Minkowski space. This generalizes Wightman's result that fields can not be defined as operators at a point and stands in contrast to Borchers' result that field operators can be associated with one-dimensional timelike planes.     

The Baxter model and scale invariant field theory

We investigate the Baxter model and its special case, the two-dimensional Ising model, within the hypothesis of an underlying scale invariant field theory. The translation of the Euclidean lattice expressions for physical operators (spinors, etc.) and pairs of the spin (order), disorder variables of the Ising model to corresponding expressions in terms of relativistic Majorana fields is carried out. All order, disorder correlation functions can be easily computed from the relativistic formulas. The generalization of such correlation functions to the Baxter model is obtained by switching on an energy-energy interaction between two Ising models. The energy-energy coupling turns out to be the Thirring coupling when linear combinations Ψ = Ψ_I + iΨ_II of Majorana fields are introduced. The critical indices α, ν, , γ and β are determined from the correlation functions and are seen to be consistent with the scaling picture.