122825959
Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories
The Rarita-Schwinger equation for a spin-$\frac{3}{2}$ particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field $\mathcal{H}$ is present. It is shown that the spectrum of energy eigenvalues includes complex values if $\mathcal{H}$ is such that $\ensuremath{\eta}\ensuremath{\equiv}(\frac{2e\mathcal{H}}{3{m}^{3}})g1$, and further that the norm of the Rarita-Schwinger wave function (i.e., the total "charge" integral defined from the Lagrangian) which is positive definite for $\ensuremath{\eta}l1$ becomes indefinite (even after taking account of the constraints) when $\ensuremath{\eta}$ exceeds unity. These results confirm that the difficulties in quantization first discovered by Johnson and Sudarshan are a reflection of the indefiniteness of the norm which appears already at the $c$-number level, and suggest that the nature of the energy spectrum (whether or not complex values are present) in the presence of very large magnetic fields would provide a quick means of predicting whether such difficulties would arise in quantization.
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...
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.
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.
18395362
QCD prerequisites for extra dimension searches
For the dilepton production at hadron collider in TeV scale gravity models, inclusion of QCD corrections to NLO stabilises the cross section with respect to scale variations. The K-factors for the various distributions for the ADD and RS model at both LHC and Tevatron are presented.
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.
15970603
Large extra dimensions and deep-inelastic scattering at HERA
Abstract In scenarios motivated by string theories, it is possible to have extra Kaluza–Klein dimensions compactified to rather large magnitudes, leading to large effects of gravity at scales down to a TeV. The effect of the spin-2 Kaluza–Klein modes on the deep-inelastic cross-section at HERA is investigated. We find that the data can be used to obtain bounds on the effective low energy scale, M S .
7785355
Getting to the top with extra dimensions
Abstract The prospect of large extra dimensions and an effective theory of gravity at around a TeV has interesting experimental consequences. In these models, the Kaluza–Klein modes interact with Standard Model particles and these interactions lead to testable predictions at present and planned colliders. We investigate the effect of virtual exchanges of the spin-2 Kaluza–Klein modes in the production cross-section of t t pairs at the Tevatron and the LHC and find that the t t cross-section can be an effective probe of the large extra dimensions. This enables us to put bounds on the effective low-energy scale.
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.