Dirac string rotations as a key to spin and statistics of dyons

The statistics of the dyonic wave functions in quantum mechanics is crucial in understanding both the fermionic behavior of the dually charged particles and the role played by the Dirac string. The spinstatistics connection for an electric-magnetic system is derived by treating the interchange operation as a 2π rotation of a singularity line of dyons. Furthermore, the invariance under multivalued gauge transformations and under change of canonical momentum representations is established for our method.     

Parity and the spin—statistics connection

A simple demonstration of the spin—statistics connection for general causal fields is obtained by using the parity operation to exchange spatial coordinates in the scalar product of a locally commuting field operator, evaluated at position x, with the same field operator evaluated at − x, at equal times.     

Local rings and the connection of spin with statistics

The usual investigations of the connection of spin and statistics start with the hypothesis that there exist only fields either commuting or anti-commuting for spacelike separations. Starting from local rings of measurements we want to show that this hypothesis can be added without loss of generality.     

Local fields with the wrong connection between spin and statistics

It is proved that there exist free field operators which satisfy local commutativity and which transform according to certain unitary representations of the homogeneous Lorentz group. The fields satisfy axioms similar to the Wightman axioms, and give rise to local algebras of observables obeying postulates similar to those suggested byHaag. They describe a tower of particles with spins 1/2, 1 1/2, 2 1/2, ..., but commute at space-like separation, giving rise to Bose statistics for the particles. This shows that the well-known theorem on spin and statistics cannot be extended to general theories of local observables; it also shows that the assumptions made in S-matrix theory do not hold for theS-matrix of a theory of interacting infinite fields.The research reported in this document has been sponsored in part by the Air Force Office ofScientific Research OAR through the European Office Aerospace Research U.S. Air Force.     

The local quantized superfield,CPT, and the connection between spin and statistics

Starting from the principles of the local quantized ordinary fields in four dimensions the theory is constructed for the local quantized superfield. From the normal connection between between spin and statistics of ordinary fields the local commutativity (anticommutativity) for superfields is obtained. Also the CPT invariance of Wightman's superfunction and the general theorem on the connection between spin and statistics are proved.     

The quantum geometry of spin and statistics

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin–statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose–Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach.     

Photon spin and Bose-Einstein statistics

It is shown that Maxwell’s equations for the electric and magnetic fields free of sources can be inferred from Dirac’s pair of first-order equations for a zero-mass, zero-charge particle. This result is interpreted as a Lorentz invariant form of the transverse nature of photonic propagation in which only two components of the spin-1 field exist in nature.Canonical quantization of Dirac’s equations leads to a time average of the electromagnetic energy in agreement with the standard result of quantum electrodynamics. It is shown that the spin-statistics theorem is not violated for canonical quantization of the Dirac field provided the mass of the particle is zero.     

Full counting statistics of spin currents

We discuss how to detect fluctuating spin currents and derive full counting statistics of electron spin transfers. We consider several detectors in series monitoring different components of the spins. We have found that in general the statistics of the measurement outcomes cannot be explained with the projection postulate and essentially depends on the quantum dynamics of the detectors.     

An algebraic spin and statistics theorem

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional spacetime. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Dedicated to Hans Borchers on the occasion of his seventieth birthdaySupported in part by MURST and CNR-GNAFA.     

A new approach to spin & statistics

We give an algebraic proof of the spin-statistics connection for the parabosonic and parafermionic quantum topological charges of a theory of local observables with a modular P₁ CT-symmetry. The argument avoids the use of the spinor calculus and also works in 1 + 2 dimensions. It is expected to be a progress towards a general spin-statistics theorem including also (1 + 2)-dimensional theories with braid group statistics.     

Extreme value statistics distributions in spin glasses

We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model, both with Gaussian and binary couplings, the distribution of the pseudocritical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like Fe(0.5)Mn)0.5)TiO(3) or Eu(0.5)Ba(0.5)MnO(3), its pseudocritical point distribution should be a priori experimentally accessible.     

Magnetic symmetry and dyons

A self-consistent theory of dyons in Abelian and non-Abelian limits has been formulated in terms of an extra magnetic symmetry and topological magnetic charge. It has been shown that the restricted gauge potential describes the fields of dyons in terms of two regular (time-like) potentials only when recourse is made to the duality of topological (magnetic) and isocolour (electric) charges. Choosing a suitable Lagrangian density for the system of dyons in non-Abelian gauge theory, the field equations, energy-momentum tensor, Hamiltonian and momentum densities have also been derived and the conservation of the four-linear momentum and the total angular momentum has been demonstrated.     

Rotating Kaluza-Klein monopoles and dyons

Conformastationary solutions of the five-dimensional vacuum Einstein equations, depending on one or two harmonic potentials, are constructed. We thus obtain solutions describing systems of rotating electric or magnetic monopoles, as well as rotating dyon solutions, satisfying the principle of equivalence.     

A block spin construction of ondelettes Part II: The QFT connection

We apply the Lemarié basis of ondelettes to the Battle-Federbush cluster expansion for the ₃ ⁴ quantum field theory. Since there is no infrared problem for this model, we also show how the large-scale ondelettes can be thrown away and replaced by unit-scale functions. Finally, we apply the block spin machine of Part I to the construction of exponentially localized ondelettes orthogonal with respect to the free, massless action of the scalar field.Supported in part by the National Science Foundation under Grant No. DMS 8603795 and by the Mathematical Sciences InstituteOn leave from the Mathematics Department, Texas A&M University, College Station, Texas 77843, USA     

Induced fractional spin and statistics in three-dimensional QED

It is shown that in background magnetic fields the fermionic Fock vacuum of (2+1)-dimensional quantum electrodynamics is a gauge invariant eigenstate of the full angular-momentum operator. The eigenvalue is computed and its relation to fractional statistics is discussed. It is argued that anomalous induced angular momentum persists to all orders in perturbation theory.