123041317
Indecomposability of poincare-group representations over massless fields, and the quantization problem for electromagnetic potentials
Considering the little group of the Poincare group associated with a lightlike four-vector, we determine explicitly, in global form, the representation of this little group over the space of covariant massless fields transforming according to some irreducible representation D (m,n) of the homogeneous Lorentz group. The little-group representation is indecomposable and nonunitary. Exploiting the knowledge of this representation for D (½, ½) (i.e., vector fields), we prove that the vector transformation property of the electromagnetic potentials A μ together with the invariance of their two-point Wightman functions (in momentum space) make it impossible to have any nontrivial scheme of quantization in which the metric is positive-definite or even semidefinite. The proof does not involve any axioms beyond those required for the definition and invariance of the Wightman functions; in particular, we do not assume the spectral condition, local commutativity, or any equations of motion or constraint.
122212810
Carruthers’ theorem for any spin and parastatistics
SummaryIt is shown that Carruthers’ theorem (that particle multiplets of half-integral isospin cannot be self-conjugate) holds even for particles which obey the general parastatistics instead of the usual Bose or Fermi statistics.RiassuntoSi dimostra che il teorema di Carruther (sull’impossibilità di autoconiugazione per multipletti di particelle con isospin semintero) value anche per particelle che obbediscono solo alla parastatistica generale invece che alla statistica consueta di Bose o Fermi.
118727721
Semi-coherent states of the quantum harmonic oscillator
SummaryIt is shown that there exists for the quantum harmonic oscillator a large class of « semi-coherent » states, which represent harmonically oscillating wave packets whose « spread » or « size » remains constant. These states are different from the coherent states in not having the minimum value 1/2ħ for the uncertainty product Δx·Δp.RiassuntoSi dimostra che esiste per l’oscillatore armonico quantistico una grande varietà di stati « semicoerenti », che rappresentano pacchetti d’onde oscillanti armonicamente, la cui « diffusione » o « dimensione » rimane costante. Questi stati differiscono dagli stati coerenti per non avere il valore minimo 1/2ħ per il prodotto d’indeterminazione Δx·Δp.РезюмеПоказывается, что для квантового гармонического осци ллятора существует б ольшой класс « полукоreр ентньIх» состояний, кот орые предст « полукоreрентньIх» состо яний, которые предста вляют гармони чески осциллирующие волновые пакеты, «разброс » или «разме ры » которых остаются постояннымгармонич ески осциллирующие волновые пакеты, «раз брос » или «размеры » которых остаются постоянными. Эти сост ояния отличаются от к огерентных состояни й тем, что не имеют мини мальной величины Р дл я произве или «размеры » которых остаются постоянными. Эти состояния отлича ются от когерентных с остояний тем, что не им еют минимальной вели чины Р для произведен ия неопределенносте й состояния отличаютс я от когерентных сост ояний тем, что не имеют минимальной величин ы Р для произведения н еопределенностей что не имеют минималь ной величины Р для про изведения неопредел енностей неопределенностей Ах Ар.
121389983
A reduction of the Kemmer equation and the singular behaviour of integer-spin relativistic Hamiltonians
Abstract A reduced form of the Kemmer equation for spin one particles is derived, wherein the wave function, which has no redundant components, transforms locally (unlike in earlier reductions). The reduced Hamiltonian is identical to the spin one specialisation of the general integer-spin Hamiltonian obtained from recent investigations on second quantizable relativistic wave equations having the Hamiltonian form. It is an observation from the present analysis that while the reduced equation is well defined for the non-zero helicity projections of the wave function, the first time derivative of the zero helicity part of the reduced wave function is essentially undefined (much as if this part described a scalar particle). This helps to explain the “improper” nature of the general Hamiltonian for integer spin.
122825959
Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories
The Rarita-Schwinger equation for a spin-$\frac{3}{2}$ particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field $\mathcal{H}$ is present. It is shown that the spectrum of energy eigenvalues includes complex values if $\mathcal{H}$ is such that $\ensuremath{\eta}\ensuremath{\equiv}(\frac{2e\mathcal{H}}{3{m}^{3}})g1$, and further that the norm of the Rarita-Schwinger wave function (i.e., the total "charge" integral defined from the Lagrangian) which is positive definite for $\ensuremath{\eta}l1$ becomes indefinite (even after taking account of the constraints) when $\ensuremath{\eta}$ exceeds unity. These results confirm that the difficulties in quantization first discovered by Johnson and Sudarshan are a reflection of the indefiniteness of the norm which appears already at the $c$-number level, and suggest that the nature of the energy spectrum (whether or not complex values are present) in the presence of very large magnetic fields would provide a quick means of predicting whether such difficulties would arise in quantization.
120479737
Arbitrary‐Spin Wave Equations and Lorentz Invariance
In an earlier paper it was shown that invariance of the arbitrary‐spin wave equation i(∂ψ/∂t) = Hψ [with ψ transforming according to the representation D(0,s)⊕D(s,0) under rotations, T, C, and P, and boosts in the direction of the momentum, permits four infinite classes of solutions for H. Here we show that when invariance under boosts transverse to the momentum also is imposed, just two possible forms for H survive (in the c‐number formalism). When we go over to the q‐number theory, one of these forms leads to a consistent theory for half‐integer spins only and the other for integer spins.
119301953
Graviton plus vector boson production to NLO in QCD at the LHC
Abstract We present the next-to-leading order QCD corrections to the associated production of the vector gauge boson ( Z / W ± ) and the graviton in the large extra dimension model at the LHC. We estimate the impact of the QCD corrections on the total cross sections as well as the differential distributions of the gauge bosons and find that they are significant. We also study the dependence of the cross sections on the arbitrary factorization scale and show the reduction in the scale uncertainties at NLO level. Further, we discuss the ultraviolet sensitivity of the theoretical predictions.
119672029
Working group report: Quantum chromodynamics
This is the report of the QCD working sub-group at WHEPP-8 which was part of the QCD and QGP working group. Discussion and work on some aspects of resummation and parton distribution are reported.
118369893
Vector boson production in association with KK modes of the ADD model to NLO in QCD at the LHC
Next-to-leading order (NLO) QCD corrections to the associated production of the vector boson (Z/W ± ) with the Kaluza-Klein (KK) modes of the graviton in large extra-dimensional model at the Large Hadron Collider (LHC) are presented. We have obtained various kinematic distributions using a Monte Carlo code which is based on the two-cutoff phase space slicing method that handles soft and collinear singularities appearing at the NLO level. We estimate the impact of the QCD corrections on various observables and find that they are significant. We also show the reduction in factorization scale uncertainty when QCD corrections are included.
7081079
PDF and scale uncertainties of various DY distributions in ADD and RS models at hadron colliders
In the extra dimension models of ADD and RS we study the dependence of the various parton distribution functions on observables of Drell–Yan processes to NLO in QCD at LHC and Tevatron energies. Uncertainties at LHC due to factorisation scales in going from leading to next-to-leading order in QCD for the various distributions get reduced by about 2.75 times for a μF range 0.5Q<μF<1.5Q. Further uncertainties arising from the error on the experimental data are estimated using the MRST parton distribution functions. 
255052
Diphoton signals in theories with large extra dimensions to NLO QCD at hadron colliders
We present a full next-to-leading order (NLO) QCD corrections to diphoton production at the hadron colliders in both standard model and ADD model. The invariant mass and rapidity distributions of the diphotons are obtained using a semi-analytical two cut-off phase space slicing method which allows for a successful numerical implementation of various kinematical cuts used in the experiments. The fragmentation photons are systematically removed using smooth-cone-isolation cuts on the photons. The NLO QCD corrections not only stabilise the perturbative predictions but also enhance the production cross section significantly.