122581187
On the gauge problem in quantum field theory
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.
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.
119207582
Next-to-next-to-leading order QCD corrections in models of TeV-scale gravity
A bstractWe compute the next-to-next-to-leading order QCD corrections to the graviton production in models of TeV-scale gravity, within the soft-virtual approximation. For the Arkani-Hamed, Dimopoulos and Dvali (ADD) model we evaluate the contribu-tion to the Drell-Yan cross section, and we present distributions for the di-lepton invariant mass at the LHC with a center-of-mass energy $ \sqrt{{{s_H}}} $ = 14 TeV. We find a large K factor (K ≃ 1.8) for large values of invariant mass, which is the region where the ADD graviton contribution dominates the cross section. The increase in the cross section with respect to the previous order result is larger than 10% in the same invariant mass region. We also observe a substantial reduction in the scale uncertainty. For the Randall-Sundrum (RS) model we computed the total single graviton production cross section at the LHC. We find an increase between 10% and 13% with respect to the next-to-leading order prediction, depending on the model parameters. We provide an analytic expression for the NNLO K factor as a function of the lightest RS graviton mass.
121827797
Finite tension strings in SU(2) gauge theory
Abstract The second-order field equations of the SU(2) Higgs model are studied and a new class of string solutions is obtained. The tension is finite and scale-dependent and the strings are of minus one unit flux.
13244174
Angular distribution of Drell–Yan process at hadron colliders to NLO-QCD in models of TeV scale gravity
In TeV scale gravity models, for dilepton production at hadron colliders, we present the NLO-QCD corrections for the double differential cross section in the invariant mass and scattering angle. For both ADD and RS models, the quantitative impact of QCD corrections for extra dimension searches at LHC and Tevatron are investigated. We present the K-factors for both ADD and RS models at LHC and Tevatron. Inclusion of QCD corrections to NLO stabilises the cross section with respect to scale variations.
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
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.