122121445
Manifest covariance without indefinite metrie in the quantization of the electromagnetic potentials
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.
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.
123558201
On inequivalent classes of unique‐mass–spin relativistic wave equations involving repeated irreducible representations with arbitrary multiplicities
Considering all representations S(Λ) of the proper Lorentz group which are equivalent to the direct sum of three unspecified inequivalent irreducible representations, each occurring with arbitrary multiplicity, the question is investigated as to what representations of the above class can support first‐order relativistic wave equations for unique‐spin, unique‐mass particles. An important requirement made from the outset is that the equation shall not be equivalent to any simpler one in the presence of arbitrary interactions. Strong restrictions which result on the irreducible representation content of S(Λ) are identified by a consideration of the Jordan canonical form of the matrix β0 entering such equations. With parity invariance as an additional requirement, it is shown that only 0 and 1 can be physical spins; classes of S(Λ) which can lead to new equations for these spins are determined. Finally, the restrictions which are needed to hold down the minimal degree of β0 to low values (≤6) are also determ...
124611352
Quantization of wave equations for zero-mass particles with invariant helicities
SummaryIn a recent paper we constructed relativistic wave equations in the standard formi∂ψ/∂t=Hψ (ψ∼D(0,s) ⊕D(s, 0)) for zeromass particles with invariant helicities. Outlining the essential steps only, we present in this short paper the details of second quantization of these equations.RiassuntoIn un recente articolo abbiamo costruito le equazioni d’onda relativistiche nella forma normalei∂ψ/∂t=Hψ (ψ∼D(0,s) ⊕D(s, 0)) per particelle di massa nulla con elicità invarianti. Delineando solo i passaggi principali presentiamo in questo breve articolo i dettagli della seconda quantizzazione di queste equazioni.РеэюмеВ недавней работе мы сконструировали релятивистские уравнения в стандартной форме i∂ψ/∂t = Нψ (ψ∼D(0, в) ⊕ D(s, 0)) для частиц нулевой массы с инвариантными спиральностями. Намечая лищь основные зтапы, мы в зтой короткой статье приводим детали только вторичного квантования зтих уравнений.
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.
121500354
Gluonic corrections to spin dependent weak structure functions
We compute gluonic corrections to the spin dependent weak structure functions g1, g3 and g4. g1WP is found o be directly proportional to the singlet part of g1μP and is ∑i(Δqi + Δqi−αsΔg/2π). In the gluon sector, g3 and g4 are both free from infrared and collinear divergences since they do not receive any gluonic corrections. Hence the Callan-Gross relation in the weak sector is nor corrected by the g→q, q subprocess. g3WP measures Δuv + Δdv. The distribution functions are identified with corresponding OPE matrix elements.
123143071
Spin determination of heavy s-channel diphoton resonances at the LHC
Diphoton events at the LHC can provide clean signals of heavy neutral quantum states predicted by New Physics models. These non-standard particles would manifest themselves by s-channel peaks in inclusive distributions in the diphoton invariant mass. Once discovered, the quantum numbers of such a diphoton resonance need to be determined in order to identify the associated non-standard physics, in the first place the spin by an angular analysis of the events. We here discuss this problem by comparing, as competing sources of a diphoton resonance, the spin-2 Randall-Sundrum graviton excitation and a spin-0 scalar exchange, by means of a specific angular-integrated asymmetry predicted theoretically at next-to-leading order in QCD. For the LHC with nominal energy of 14 TeV and integrated luminosity 100 fb−1, we find that graviton exchange could be discriminated against the scalar one with same mass MR and events rate, up to MR≃3.2TeV.
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.
15970603
Large extra dimensions and deep-inelastic scattering at HERA
Abstract In scenarios motivated by string theories, it is possible to have extra Kaluza–Klein dimensions compactified to rather large magnitudes, leading to large effects of gravity at scales down to a TeV. The effect of the spin-2 Kaluza–Klein modes on the deep-inelastic cross-section at HERA is investigated. We find that the data can be used to obtain bounds on the effective low energy scale, M S .
14620818
Unparticle physics at hadron collider via dilepton production
The scale invariant unparticle physics recently proposed by Georgi could manifest at low energies as non-integral number dU of invisible particles. Unparticles if existing, could couple to the Standard Model fields and consequently affect the collider phenomenology. We consider the DY process to explore effects of the peculiar propagator of the scalar and tensor unparticle operators. To probe these effects at hadron collider one needs to go beyond LO in QCD and hence the quantitative impact of QCD corrections for unparticle physics at LHC is investigated. We present the K-factors at LHC. Inclusion of QCD corrections to NLO stabilises the cross section with respect to scale variations.