120046449
Evaluation of the density matrix for an ensemble of anharmonic oscillators by a path integral approach
Considering the Feynman path integral representation for the configuration-space density matrix for an ensemble of anharmonic oscillators, we determine the ‘stationary paths’ near which the integrand remains stationary. By taking the path integral to be saturated by contributions from the neighborhood of the path which maximizes the integrand we evaluate the density matrix explicitly in analytic form. This seems to be the first such evaluation of a path integral for a system not describable by a quadratic Hamiltonian. We also comment briefly on the question of analyticity with respect to the perturbation parameter.
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...
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.
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.
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.
119114678
Diphoton production in the ADD model to NLO + parton shower accuracy at the LHC
A bstractIn this paper, we present the next-to-leading order predictions for diphoton production in the ADD model, matched to the HERWIG parton shower using the MC@NLO formalism. A selection of the results is presented for d = 2–6 extra dimensions, using generic cuts as well as analysis cuts mimicking the search strategies as pursued by the ATLAS and CMS experiments.
14620818
Unparticle physics at hadron collider via dilepton production
The scale invariant unparticle physics recently proposed by Georgi could manifest at low energies as non-integral number dU of invisible particles. Unparticles if existing, could couple to the Standard Model fields and consequently affect the collider phenomenology. We consider the DY process to explore effects of the peculiar propagator of the scalar and tensor unparticle operators. To probe these effects at hadron collider one needs to go beyond LO in QCD and hence the quantitative impact of QCD corrections for unparticle physics at LHC is investigated. We present the K-factors at LHC. Inclusion of QCD corrections to NLO stabilises the cross section with respect to scale variations.
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.
121522381
GLUONIC CONTRIBUTIONS TO SPIN-DEPENDENT WEAK STRUCTURE FUNCTIONS: METHOD OF FACTORIZATION
We compute the gluonic contributions to the spin-dependent weak structure functions (i=1, 3, 4), using the factorization theorem in the minimal subtraction scheme, . We have considered the most general case where the quark flavor masses are distinguished and the gluons are off mass shell. The gluonic contribution to the first moment of is found to vanish and do not receive leading order gluonic contribution. These results are shown to be free of mass singularities.
121477714
Publisher's Note: Unparticle physics in diphoton production at the CERN LHC [Phys. Rev. D 77, 055013 (2008)]