Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics

Given the local observables in the vacuum sector fulfilling a few basic principles of local quantum theory, we show that the superselection structure, intrinsically determined a priori, can always be described by a unique compact global gauge group acting on a field algebra generated by field operators which commute or anticommute at spacelike separations. The field algebra and the gauge group are constructed simultaneously from the local observables. There will be sectors obeying parastatistics, an intrinsic notion derived from the observables, if and only if the gauge group is non-Abelian. Topological charges would manifest themselves in field operators associated with spacelike cones but not localizable in bounded regions of Minkowski space. No assumption on the particle spectrum or even on the covariance of the theory is made. However the notion of superselection sector is tailored to theories without massless particles. When translation or Poincaré covariance of the vacuum sector is assumed, our construction leads to a covariant field algebra describing all covariant sectors.Research supported by Ministero della Pubblica Istruzione and CNR-GNAFA     

Enlarged Peccei-Quinn symmetry and limits from the supernova

We construct a model generalizing the invisible axion model of Dine, Fischler and Srednicki to three scalar doublets and two scalar singlets. By imposing two U(1) symmetries rather than the single Peccei-Quinn symmetry of the DFS model, we arrive at a physical particle spectrum containing both a light axion and a massless Goldstone boson. The axion couplings are as usual suppressed by a large VEV, which is bounded below by SN1987a emission limits and above by cosmological arguments. The VEV in the Goldstone boson couplings is bounded below by SN1987a emission and subsequent conversion into gamma rays via the galactic magnetic field, but the cosmological upper bound cannot be applied to this massless boson.     

Electromagnetic fields and potentials generated by massless charged particles

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ$\delta$-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ$\delta$-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string.     

TWO-DIMENSIONAL ANGULAR MOMENTUM AND FERMION IN THE FIELD OF MAGNETIC-FLUX-TUBE

In this paper, we showed that the eigenvalues of two-dimensional angular momentum of a particle with charge a are integer valued. The problems of a Dirac particle in a field of vortex were discussed. When the vortex tends-to string, we found that the system admits of the existence of θ vacua. For massless fermions, a change in θ is equivalent to a Γ_s rotation, while the physical result is independent of θ. For massive fermions, CP invariance is broken except for θ=0,π; and the system exhibits the Witten effect.     

Spinor fields with zero mass in unbounded isotropic media

The Dirac equation for massless fields in unbounded media has solutions similar to the focus wave mode solutions of Maxwell's equations leading to infinite dynamical invariants. We define the splash wave mode solutions as a weighted superposition of the focus wave modes, and discuss the conditions to be fulfilled by the weight functions to make the dynamical invariants bounded. We leave open the physical interpretation of these solutions.     

On the Motion of a Small Light Body Immersed in a Two Dimensional Incompressible Perfect Fluid with Vorticity

In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the “fluid+rigid body” system converges to the vortex-wave system introduced by Marchioro and Pulvirenti (Mathematical theory of incompressible nonviscous fluids. Applied Mathematical Sciences 96, Springer-Verlag, 1994). This extends both the paper (Glass et al. Bull Soc Math France 142(3):489–536, 2014) where the case of a solid tending to a massive pointwise particle was tackled and the paper (Glass et al. Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid, 2014) where the massless case was considered but in a bounded cavity filled with an irrotational fluid.     

Systems of covariance and subrepresentations of induced representations

In relativistic quantum physics, systems of covariance are used to describe the localizability of massless elementary systems. The notion of a system of covariance generalizes that of a system of imprimitivities by replacing the projection valued measure by a positive operator valued measure. Our main result concerns the constructibility of systems of covariance from systems of imprimitivities on different premises. As a corollary we get an analogous theorem to Mackey's Imprimitivity Theorem characterizing subrepresentations of induced representations.     

New class of N-dimensional braneworlds

The new class of the non-stationary solutions to the system of N-dimensional equations for coupled gravitational and massless scalar field is found. The model represents a single (N-1)-brane in a space-time with one large (infinite) and (N-5) small (compact) space-like extra dimensions. In some particular cases the model corresponds to the gravitational and scalar field standing waves bounded by the brane. These braneworlds can be relevant in string and other higher dimensional models.     

Lorentz Covariant Canonical Formalism for Free Massive, Massless and Tachyonic Particles

We construct a consistent Lorentz-covariant canonical formalism for a free massive, massless and tachyonic particle in the framework of the absolute synchronization scheme of clocks. In the case of a massive particle our approach is canonically equivalent to the standard formulation which is not manifestly covariant. The absolute synchronization scheme seems to be the only one we can apply in the case of massless and tachyonic particles.     

超导与规范对称性,希格斯机制与希格斯粒子——电磁学与电动力学中的超导Ⅱ

本文是文献[1]和[2]联合的后继文章,在文中我们依据电磁学和电动力学中的麦克斯韦方程组建立了有质量光子导致导体中的超导现象这一事实的规范不变描写,文献[1]的结果是目前理论选取洛伦兹规范的特殊情形.我们发现在这种规范不变的理论中存在一个零质量的标量场,它可以和规范势的纵向分量相互转化.这正是文献[2]所介绍的2013年诺贝尔物理学奖中著名的希格斯机制,即规范粒子吃掉Goldstone玻色子而产生纵向分量,因而获得质量.这个新引进的零质量标量场对应量子场论中激发Goldstone玻色子的标量场,它可以被看成是一个更一般的两分量复标量场的相角分量.而此推广的复标量场的常数模分量可以被看成是另一个动力学场——希格斯场的真空期望值.希格斯场的激发是希格斯粒子,即所谓上帝的粒子;而光子的质量则起源于希格斯场的真空期望值.     

Integrable quantum field theories and Bogoliubov transformations

The Federbush, massless Thirring and continuum Ising models and related integrable relativistic quantum field theories are studied. It is shown that local and covariant classical field operators exist that generate Bogoliubov transformations of the annihilation and creation operators on the Fock spaces of the respective models. The quantum fields of these models are closely related or equal to quadratic forms implementing these transformations, and hence formally inherit the covariance and locality of the underlying classical field operators. It is proved that the Federbush and massless Thirring fields on the physical sector do not satisfy the equation of motion. Closely related fields are defined that do satisfy it, and which lead to the same S-matrix, but these fields are presumably non-local. Bethe transforms are constructed for the various models, and on the unphysical sector the relation with the field theory approach is established.     

Thermal representation of the energy density in bounded spaces

The energy-momentum tensor of a quantum massless free field in a curved spacetime can be written in many cases as an integral with a thermal denominator and a modified phase-space numerator. It is shown that in general the thermal denominator is related to the bounded nature of the system, which in turn implies a representation of the energy density as an infinite numerable sum in Fock space. The modification of the phase-space density is related to the absence of long-wave contributions for nonzero values of the spin.