121298874
Dynamics of a nonlinear field
Abstract A systematic study is made of the plane wave modes of a nonlinear c -number field ( λφ 4 model) and interesting features of the behavior of such fields, which do not seem to have been observed before, are brought out. These relate to the case λ lower bound on the energy density in the wave field. The case of fields with higher nonlinearities is briefly considered.
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.
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.
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.
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.
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 .
16629741
PHOTON STRUCTURE FUNCTIONS: TARGET PHOTON MASS EFFECTS AND QCD CORRECTIONS
We present a systematic analysis of the polarized and unpolarized processes e+e−→ e+e−X in the deep inelastic limit and study the effect of target photon mass (virtuality) on the photon structure functions. The effect of target photon virtuality manifests itself as new singly polarized structure functions, and also alters the physical interpretation of the unpolarized structure functions. The physical interpretation of these structure functions in terms of hadronic components is studied using the free field analysis. We also retrieve the real photon results in the limit where the virtuality goes to zero. Assuming factorization of the photon structure tensor, the relevant QCD corrections to the various twist 2 structure functions are evaluated.
7785355
Getting to the top with extra dimensions
Abstract The prospect of large extra dimensions and an effective theory of gravity at around a TeV has interesting experimental consequences. In these models, the Kaluza–Klein modes interact with Standard Model particles and these interactions lead to testable predictions at present and planned colliders. We investigate the effect of virtual exchanges of the spin-2 Kaluza–Klein modes in the production cross-section of t t pairs at the Tevatron and the LHC and find that the t t cross-section can be an effective probe of the large extra dimensions. This enables us to put bounds on the effective low-energy scale.
118428442
Associated production of vector gauge boson & graviton to NLO QCD
In this talk, we discuss the next-to-leading order (NLO) QCD corrections to the associated production of the vector gauge boson (Z/W ± ) and the graviton in the large extra dimension model, namely the ADD model, at the LHC. After a brief review of the ADD model, we present the importance of QCD correction to these preferred processes and the impact of the QCD corrections on the total cross sections as well as the differential distr ibutions of the gauge bosons. The dependence of the cross sections on the arbitrary factorization s cale is studied and the reduction in the scale uncertainties at NLO level is shown. The ultraviolet sensitivity of the theoretical prediction is also presented.
119185858
Neutral triple electroweak gauge boson production in the large extra-dimension model at the LHC
We study the prospects of probing large extra dimension model at the LHC through neutral triple gauge boson production processes. In theories with extra dimensions these processes result from the exchange of a tower of massive graviton modes between the SM particles. We consider \gamma\gamma\gamma, \gamma \gamma Z, \gamma Z Z and ZZZ production processes, and present our results for various kinematic distributions at the LHC for \sqrt{S}=14 TeV.