118460186
A quantum-mechanically solvable nonpolynomial Lagrangian with velocity-dependent interaction
SummaryThe quantum-mechanical problem of the nonlinear oscillator with the Lagrangian L= 1/2 [x2-k0x2)/(l-λx2)] is solved exactly and the energy levels and eigenfunctions are obtained completely. This model (whenk0=0) is the zero-space-dimensional isoscalar analogue of the nonlinearSU2⊗ SU2 chirally invariant Lagrangian in the Gasiorowicz-Geffen co-ordinates and may also be considered as a modified version of the anharmonic-oscillator and Lee-Zumino models. The bound-state energy levels are found to have a linear dependence on the coupling parameter, in sharp contrast to the case of the familiar oscillator With quartic anharmonicity where the energy, as a function of λ, has complicated singularities at λ = 0. We investigate how far certain standard approximation procedures reproduce the exact results. The Bohr-Sommerfeld quantization procedure is found to reproduce the form of the boundstate energy levels correctly. Interestingly a perturbation-theoretic treatment also reproduces the correct results at least up to the order (λ2) to which we have carried our calculations.RiassuntoSi risolve esattamente il problema della meccanica quantistica dell’osoillatore non lineare con lagrangianoL = 1/2 [(x2-k0x2)/(l-λx2)] e se ne ottengono completamente le autofunzioni e i livelli energetici. Questo modello (quandok0 = 0) è l’analogo isoscalare con dimensione spaziale nulla del lagrangiano chiralmente invarianteSU2 ⊗ SU2 non lineare nelle coordinate di Gasiorowicz-Greffen e si può anche considerare come una versione modificata dei modelli dell’oscillatore anarmonico e di Lee-Zumino. Si trova che i livelli energetici di stato legato dipendono linearmente dal parametro di accoppiamento, in evidente contrasto con il caso familiare di oscillatore con anarmonicità del quart’ordine in cui l’energia, espressa in funzione di λ, presenta complicate singolarità per λ = 0. Si cerca di vedere sino a che punto certi procedimenti standard di approssimazione riproducono i risultati esatti. Si trova che il metodo di quantizzazione di Bohr-Sommerfeld riproduce correttamente la forma dei livelli di energia degli stati legati. È interessante che anche un trattamento con la teoria delle perturbazioni riproduca correttamente i risultati almeno fino all’ordine (λ2) al quale si sono spinti i calcoli.РезюмеТочно решается квант овомеханическая проблема нелинейног о осциллятора с Лагранжианом 

$$L = \frac{1}{2}\left[ {(x^2 - k_0 x^2 )/\left( {1 - \lambda x^2 } \right)} \right]$$

. Полу чены уровни энергии и собственные функции. Эта модель (когда k0=0) представляет изоска лярный аналог с нулевой пространст венной размерностью для нелинейногоSU2⊗SU2, ки рально инвариантного Лагра нжиана в координатах Газиоровича-Геффена и может рассматриват ься как модифицированны й вариант ангармонич еского осциллятора и моделей Ли-Зумино. Обн аружено, что энергети ческие уровни связанных сос тояний имеют линейную завис имость от параметра с вязи в противоположность с лучаю обычного осциллятор а с квадратичной ангармоничностью, дл я которого энергия, как функция Л, имеет си нгулярность при λ=0. Мы исследуем, насколько процедуры стандартных приближ ений воспроизводят т очные результаты. Получено, что процедура квантования Бора-Зом мерфельда правильно воспроизводит форму энергетических уровней свазанных со стояний. Интересно от метить, что в теории возмущений также получаются пра вильные результаты, п о крайней мере, до порядка (λ2), в ко тором мы производили наши в ычисления.
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...
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.
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.
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.
125692178
Probing gluon and sea spin in proton
8021098
Next-to-leading order QCD corrections to the Drell-Yan cross section in models of TeV-scale gravity
Abstract The first results on next-to-leading order QCD corrections to graviton-induced processes in hadron collisions in models of TeV-scale gravity are presented focusing on the case of dilepton pair production in p ¯ p and pp collisions. Distributions in the invariant mass Q , the longitudinal fraction x F , the rapidity Y and the forward–backward asymmetry of the lepton pair are studied. The quantitative impact of the QCD corrections for searches of extra dimensions at hadron colliders is investigated. It turns out that at the LHC ( S = 14  TeV ) the K -factor is rather large ( K = 1.6 ) for large invariant mass Q of the lepton pair, indicating the importance of accounting for these QCD corrections in the experimental search for TeV-scale gravity. At the Tevatron, the K -factor does not substantially deviate from the Standard Model value. However, its inclusion is necessitated to make the cross section stable with respect to scale variations.
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.
21626154
Three photon production to NLO+PS accuracy at the LHC
In this paper, we present the next-to-leading order predictions for three photon production in the standard model, matched to the parton shower using the MC@NLO formalism. We have studied the role of the parton shower on various observables and we show a selection of results for the $$14$$14 TeV Large Hadron Collider.
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. 