118914003
Wave equations for zero-mass particle with invariant helicities
SummaryWe present a brief discussion of the difficulties associated with taking the limitm→0 in massive-particle equations of the formi(∂ψ/∂t)=Hψ, in which ψ transforms according to theD(0,s)⊕D(s,0) representation of the homogeneous Lorentz group. It is pointed out that, though the HamiltonianH tends to a well-defined form asm→0, the resulting wave equation is still unsatisfactory as the invariant scalar product (in the space of solutions of the wave equation) has an unacceptable form. We observe that this difficulty is due to the indecomposability of the representation of the Poincaré group over wave functions transforming asD(0,s)⊕D(s,0) in the massless case. Making due allowance for this fact we obtain, in close parallel to the treatment for massive particles, wave equations for zero-mass particles with invariant helicities ±s. The relevant invariant scalar products are also determined.RiassuntoSi presenta una breve discussione associata con il limitem→0 in equazioni per particelle con massa della formai(∂ψ/∂t)=Hψ, in cuiψ si trasforma secondo la rappresentazioneD(0,s)⊕C(s,0) del gruppo di Lorentz omogeneo. Si mette in rilievo che, sebbene l’hamiltonianoH tenda ad una forma ben definita quandom→0, l’equazione d’onda risultante non è ancora soddisfacente in quanto il prodotto scalare invariante (nello spazio delle soluzioni dell’equazione d’onda) ha una forma inaccettabile. Si osserva che questa difficoltà è dovuta alla indecomponibilità della rappresentazione del gruppo di Poincaré rispetto alle funzioni d’onda che si trasformano comeD(0,s)⊕D(s, 0) nel caso senza massa. Tenendo dovuto conto di questo fatto si ottengono, in stretta analogia con il trattamento per particelle con massa, equazioni per particelle con massa nulla con elicità invarianti ±s. Si determinano anche i relativi prodotti scalari invarianti.РеэюмеВкратце обсуждаются трудности, воэникаюшие при переходе к пределуm→;0 в уравнениях видаi(∂ψ/∂t)=H у с отличной от нуля массой частиц, в которых ψ преобраэуется согласно представлениюD(0,s)⊕D(s, 0) однородной группы Лорентца. Отмечается, что хотя Гамильтониан Я стремится к хорощо иэвестному выражению приm→0, но окончательное волновое уравнение является неудовлетворит ельным, так как инвариантное скалярное проиэведение (в пространстве рещений волнового уравнения) имеет неприемлемый вид. Мы обнаруживаем, что зта трудность обусловлена неприводимостью представления группы Пуанкаре череэ волновые функции, преобраэуюшиеся, какD(0,s)⊕D(s,0) в случае нулевой массы. Учитывая зтот факт, мы, по аналогии с рассмотрением для частиц с отличной от нуля массой, получаем волновое уравнение для частиц нулевой массы с инвариантными спиральностями ±s. Также определяются соответствуюшие инвариантные скалярные проиэведения.
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.
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.
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...
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.
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.
1741127
Dijet production at the LHC through unparticles
We report the phenomenological impact of unparticles in the production of dijet at the LHC. We compute the scalar, spin-1 and spin-2 unparticle contributions to the dijet cross sections and present our results in different kinematical distributions. We find that the scalar unparticle contribution is dominant over that of the spin-1 and spin-2 unparticles for the same coupling values.
123143071
Spin determination of heavy s-channel diphoton resonances at the LHC
Diphoton events at the LHC can provide clean signals of heavy neutral quantum states predicted by New Physics models. These non-standard particles would manifest themselves by s-channel peaks in inclusive distributions in the diphoton invariant mass. Once discovered, the quantum numbers of such a diphoton resonance need to be determined in order to identify the associated non-standard physics, in the first place the spin by an angular analysis of the events. We here discuss this problem by comparing, as competing sources of a diphoton resonance, the spin-2 Randall-Sundrum graviton excitation and a spin-0 scalar exchange, by means of a specific angular-integrated asymmetry predicted theoretically at next-to-leading order in QCD. For the LHC with nominal energy of 14 TeV and integrated luminosity 100 fb−1, we find that graviton exchange could be discriminated against the scalar one with same mass MR and events rate, up to MR≃3.2TeV.
125601151
Spin identification of the RS resonance in di-photon production to NLO at the LHC
6977127
Probing Large Extra Dimensions Using Top Production in Photon-Photon Collisions
Theories with large extra dimensions predict an infinite tower of Kaluza-Klein states in the 1 TeV range, which can consequently have significant implications for experimental observables. One such