119726764
On the degree of the minimal equation of the matrices in first-order relativistic wave equations
Starting with an analysis of the general structure of the matrix beta 0 entering in first-order relativistic wave equations, the authors show that the degree of the minimal equation of beta 0 is determined by the size and nature of the various spin blocks of the 'skeleton matrix' of the theory. Since it is the numbers of Lorentz irreducible representations contributing to particular spins which determine the sizes of the spin blocks (and the value jm of the maximum spin contained in psi has no direct bearing on these), the reason for the failure of the Umezawa-Visconti rule and its extrapolation by Chandrasekaran et al. (1972) becomes clear. The authors obtain some general results concerning the minimal degree in certain types of theories and on certain procedures whereby the minimal degree can be raised without altering jm, and finally analyse a few interesting examples.
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.
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...
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.
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.
11061527
{chi}{sub 1} and polarization asymmetries for quarkonia at high orders in nonrelativistic QCD
We study doubly polarized asymmetries of {bar c}c and {bar b}b mesons in hadroproduction and photoproduction at low transverse momentum in nonrelativistic QCD to high orders in the relative velocity of the pair, v. We give the complete set of expressions required for the asymmetries up to order v{sup 9}. The asymmetries in the production of {eta}{sub c,b} states are a stable measure of the polarized gluon densities. The asymmetries for {chi}{sub c,b}, J/{psi}, {psi}{sup {prime}}, and the various {Upsilon} states are stringent tests of the NRQCD scaling relations. {copyright} {ital 1997} {ital The American Physical Society}
15386012
Searching for signals of minimal length in extra dimensional models using dilepton production at hadron colliders
Theories of quantum gravity suggest the existence of a minimal length scale. It is interesting to speculate what the consequences of the existence of such a length scale would be for models of large extra dimensions, in particular, the ADD model. When ADD model is conflated with the minimal length scale scenario, processes involving virtual exchange of gravitons cease to be ulraviolet divergent. We study the production of dileptons at hadron colliders as an example of a process mediated by virtual gravitons. We find that the bounds we derive on the effective string scale are significantly different (in fact, less stringent) from those derived in the conventional ADD model, both at the upgraded Tevatron and the large hadron collider.
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.
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.
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.