120740147
Relativistic wave equations: proper Lorentz invariance and invariance under discrete transformations
Considering the standard form i∂ψ/∂t=Hψ [with ψ transforming according to D(0,s)⊕D(s,0)] of wave equations for free particles of arbitrary spin, we determined in a recent paper the admissible forms of H consistent with invariance of the equation under the Poincare group and under T, C, and P. Here we show that even if T and C invariance is not imposed, the admissible Hamiltonians are the same (apart from one extra possibility H = E). Expressed differently, except for the trivial case H = E, invariance of free‐particle equations under the connected Poincare group and P implies T and C also.
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.
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...
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.
125974090
Tri-vector boson production at NLO with parton shower
We have studied the production of three photons at the LHC taking into account realistic experimental cuts. We have used NLO corrected QCD results for the production mechanism along with parton showering through HERWIG and Pythia. This is achieved using aMC@NLO framework which uses FKS subtracton method through MadFKS to handle infrared singularities present in the intermediate stages of NLO computation. We find that the results at NLO level in QCD with parton showering show less PDF and factorisation scale dependence.
10218302
Unparticle physics in diphoton production at the CERN LHC
We have considered the diphoton production in the unparticle physics at the LHC. The contributions of spin-0 and spin-2 unparticles to the diphoton production are studied in the invariant mass and other kinematical distributions, along with their dependencies on the model dependent parameters. It is found that the signal corresponding to the unparticles is significant for moderate values of the couplings.
18381800
Can polarized Drell-Yan shed more light on the proton spin
We analyze polarized Drell-Yan process using the factorization method and derive operator definitions for polarized parton distribution functions. We demonstrate that a factorization analogous to that in the unpolarized Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarized Drell-Yan function and show that it is consistent with the results obtained from polarized deep inelastic scattering.
54538817
Quark and gluon spin-2 form factors to two-loops in QCD
A bstractWe present complete two-loop radiative corrections to the graviton-quark-antiquark form factor G∗ → q$ \overline{q} $ and graviton-gluon-gluon form factor G∗ → g g in SU(N) gauge theory with nf light flavours using d-dimensional regularisation to all orders in ε = d − 4. Thisisanimportantingredienttonext-to-next-to-leadingorderQCDcorrections to hadronic scattering processes in models with large extra-dimensions where Kaluza-Klein graviton modes couple to Standard Model fields. We show that these form factors obey Sudakov integro-differential equation and the resulting cusp, collinear and soft anomalous dimensions coincide with those of electroweak vector boson and gluon form factors. We also find the universal behaviour of the infrared singularities in accordance with the proposal by Catani.
16849310
Extra Dimensions: A View from the Top
In models with compact extra dimensions, where the Standard Model fields are confined to a 3+1 dimensional hyperplane, the tt̄ production cross-section at a hadron collider can receive significant contributions from multiple exchange of KK modes of the graviton. These are carefully computed in the well-known ADD and RS scenarios, taking the energy dependence of the sum over graviton propagators into account. Using data from Run-I of the Tevatron, 95% C.L. bounds on the parameter space of both models are derived. For Run-II of the Tevatron and LHC, discovery limits are estimated. ∗Magda.Lola@cern.ch †mathews@it.unesp.br ‡sreerup@iitk.ac.in, sreerup@mail.cern.ch §sridhar@theory.tifr.res.in In recent years, there has been tremendous interest in higher dimensional theories where the extra dimensions are compactified in such a way as to have physically interesting consequences[1]. These have been inspired by recent developments in our understanding of some non-perturbative aspects of string theories. The weak-coupling spectrum of such a theory reveals only one-dimensional strings but, in the strong coupling regime, p+1 dimensional defects embedded in the higher-dimensional spacetime — called Dp-branes — arise. These are dynamical objects analogous to solitons in field theory and are particularly interesting because it is possible to localize gauge fields on them. We then have the exciting possibility that the observable universe is a D3-brane (or 3-brane) with the Standard Model (SM) fields localized on it, leaving gravity free to propagate in the extra dimensions or bulk. In such a scenario, it becomes possible to lower the gravity/string scale to the order of a TeV, without running into contradiction with experiment. This new TeV-scale physics then provides fresh perspectives on the hierarchy problem arising in the standard electroweak theory. The first realization of these ideas is the ADD scenario proposed by Arkani-Hamed, Dimopoulos and Dvali[2], where the SM fields are localized on a 3-brane embedded in a 10-dimensional spacetime consisting of 4 non-compact Minkowski dimensions, d dimensions compactified with a large radius Rc and the remaining 6 − d dimensions compactified to the Planck length. The Planck scale MP is then related[2] to the scale MS of gravitational interactions by MP ∼ R cM S . Choosing the scale MS to be of the order of a TeV (which eliminates the usual hierarchy problem) it follows that Rc ∼ 1032/d−19 m. This immediately precludes d = 1, but for any value d > 1, we find that MS can be arranged to be a TeV for compactification radii as large as a millimetre, without confliciting with gravity experiments[3]. Effects of non-Newtonian (quantum) gravity can then become apparent at these surprisingly low values of energy. While it is possible[4] to construct a physically viable scenario with large Rc which can survive the existing astrophysical and cosmological constraints, such a scenario inevitably predicts large deviations from the SM in several low-energy effects [5]. Thus, laboratory data can be used to derive [5] bounds on MS in the TeV range — though some astrophysical bounds can, in fact, be considerably stronger [6]. The main criticism of the ADD scenario is the reappearance of a large hierarchy between the string scale MS ∼ 1 TeV and the compactification radius Rc ∼ (10−16 TeV)−1, which makes it difficult to stabilize the size of the large extra dimensions. This has inspired the RS scheme — proposed by Randall and Sundrum [7] — where only a single extra dimension is invoked. This fifth dimension φ is strongly curved and is compactified on a S/Z orbifold with a radius Rc, which is assumed to be somewhat larger than the Planck length. Two 3-branes are located at the orbifold fixed points: a ‘Planck brane’ at φ = 0 and a ‘TeV brane’ at φ = π. The tension on the branes and the cosmological constant in the bulk are fine-tuned to give a flat (Minkowski) geometry on the 3-branes. The bulk metric that guarantees this