On the geometry of reduced cotangent bundles at zero momentum

We consider the problem of cotangent bundle reduction for proper non-free group actions at zero momentum. We show that in this context the symplectic stratification obtained by Sjamaar and Lerman refines in two ways: (i) each symplectic stratum admits a stratification which we call the secondary stratification with two distinct types of pieces, one of which is open and dense and symplectomorphic to a cotangent bundle; (ii) the reduced space at zero momentum admits a finer stratification than the symplectic one into pieces that are coisotropic in their respective symplectic strata.     

The zero momentum limit of the vacuum polarization at finite temperature

We examine the zero momentum limit of the finite temperature vacuum polarization for a quantized scalar field coupled to a classical external field. Ordinarily, this type of Feynman diagram is plagued by nonanalytic behaviour when the external momentum tends to zero. Using imaginary-time, we show that this behaviour is not present in an exact background field solution and how the Feynman diagram calculation may be trivially modified to match the exact solution. Comparisons with recent real-time results are also made.     

Spontaneous symmetry breaking at infinite momentum without P+ zero modes

The nonrelativistic interpretation of quantum field theory achieved by quantization in an infinite momentum frame is spoiled by the inclusion of a mode of the field carrying p(+) = 0. We therefore explore the viability of doing without such a mode in the context of spontaneous symmetry breaking (SSB), where its presence would seem to be most needed. We show that the physics of SSB in scalar quantum field theory in 1+1 space-time dimensions is accurately described without a zero mode.     

The normal liquid 3He one-body momentum distribution at zero and finite temperature

The normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism. The lowest order constrained variational (LOCV) and the extended LOCV (ELOCV) method are used to calculate the correlation functions at zero and finite temperatures. The input inter-atomic potential is the familiar 6–12 Lennard-Jones interaction. The gap in n(k) at the Fermi surface is found to be about 0.41 comparing to 1.0 (0.72) for the noninteracting (dilute hard-sphere) Fermi gas model at zero temperature and it decreases by increasing the temperature. It is also demonstrated that the high-momentum tail of n(k) gets larger as we increase the temperature and finally, we find a good agreement between present calculated n(k) and those coming from more sophisticated approaches such as Diffusion and Green-function Monte Carlo techniques.     

The Fourier-Bessel expansion of the scattering amplitude at zero momentum transfer for particles with unequal mass

We investigate the problem of whether a Fourier-Bessel type expansion can be valid at zero-momentum transfer for the unequal-mass scattering amplitude, as a substitute for the Regge-Watson-Sommerfeld representation. It is shown that the results of a previous paper, giving the solution of the same problem for amplitudes satisfying an unsubtracted dispersion relation can be extended to a class of asymptotically growing scattering amplitudes. In the second part of the paper a Lorentz-pole expansion is outlined, which is valid at arbitrary momentum transfer. The expansion coefficients of this last expansion are expressed by means of the discontinuities of the amplitudes. Finally, a comparison is made between the Fourier-Bessel expansion and the Lorentz expansion. We argue that, at least as far as the unequal-mass formulas are concerned, it is highly unnatural to assume that a pomeron with intercept α(0) = 1 belongs purely to the four-vector representation of the Lorentz group. Rather, it is a mixed object belonging to the four-dimensional and the accompanying infinite-dimensional ones, both characterized by the same Casimir operator eigenvalues.     

Rotation of laser beams with zero of the orbital angular momentum

We show that among the multitude of rotating light beams whose complex amplitude can be represented as a linear superposition of the Laguerre-Gaussian (LG) modes with definite numbers there are light beams with zero orbital angular momentum (OAM) and vice versa, multi-mode LG beams that show no rotation and are lacking the radially symmetric intensity distribution can possess the non-zero OAM. Also, we give examples of the rotating light beams with zero OAM, represented as a superposition of the Bessel and new hypergeometric modes. Using an SLM, we generate a rotating Bessel beam with zero OAM for the first time.     

On the extraction of zero momentum form factors on the lattice

We propose a method to expand correlation functions with respect to the spatial components of external momenta. From the coefficients of the expansion it is possible to extract Lorentz-invariant form factors at zero spatial momentum transfer avoiding model dependent extrapolations. These objects can be profitably calculated on the lattice. We have explicitly checked the validity of the proposed procedure by considering two-point correlators with insertions of the axial current, the form factors of the semileptonic decay of pseudoscalar mesons, and the hadronic vacuum polarization tensor entering, for example, the lattice calculation of the anomalous magnetic moment of the muon.     

Control of atomic rotation by elliptical hollow beam carrying zero angular momentum

The interaction between linearly polarized elliptical hollow beam and a two-level atom is investigated theoretically. Although the linearly polarized elliptical hollow beam does not carry angular momentum, it can produce very high torque. The atoms initially at rest and located at off-beam-axis positions will rotate under the drive of the torque of the beam. The shorter the distance from the original location of atom to the axis is, the larger the average angular frequency of atom rotation is. The average angular frequency can reach as high as 1000 Hz. This convinces us that the elliptical hollow beam might be a useful tool in the study of quantum property of Bose–Einstein condensate or ultra cold atom media.     

Calculation of Feynman diagrams with zero mass threshold from their small momentum expansion

A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large compared to all momenta squared). Using dimensional regularization, a finite result is obtained in terms of powers of logarithms (describing the zero-threshold singularity) times power series in the momentum squared. Surprisingly, these latter ones represent functions, which not only have the expected physical “second threshold” but have a branchcut singularity as well below threshold at a mirror position. These can be understood as pseudothresholds corresponding to solutions of the Landau equations. In the spacelike region the imaginary parts from the various contributions cancel. For the two-loop examples with one mass M, in the timelike region for q² ≈ M² we obtain approximations of high precision. This will be of relevance in particular for the calculation of the decay Z → bb?in the m _b = 0 approximation.     

What does low energy physics tell us about the zero momentum gluon propagator

The connection between QCD, a nonlocal Nambu–Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson–Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, Γ_π→γγ${\Gamma }_{\pi \to \gamma \gamma }$ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson–Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of the above scenarios. Furthermore, the nonlocal Nambu–Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.     

Entanglement energetics at zero temperature

We show how many-body ground state entanglement information may be extracted from subsystem energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show that this type of measurement provides another method to quantify entanglement with the environment.     

Coulomb drag at zero temperature

We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is of the order h/(e2g3), where g is the dimensionless sheet conductance. The effect is therefore the strongest in low mobility samples. This behavior should be contrasted with the conventional (second order) prediction that the transresistance scales as a certain power of temperature and is (almost) mobility independent. The result demonstrates that the zero-temperature drag is not an unambiguous signature of a strongly coupled state in double-layer systems.     

Multi-lepton production at high transverse momentum at HERA

A search for events containing two or more high-transverse-momentum isolated leptons has been performed in ep collisions with the ZEUS detector at HERA using the full collected data sample, corresponding to an integrated luminosity of 480 pb⁻¹. The number of observed events has been compared with the prediction from the Standard Model, searching for possible deviations, especially for multi-lepton events with invariant mass larger than 100 GeV. Good agreement with the Standard Model has been observed. Total and differential cross sections for di-lepton production have been measured in a restricted phase space dominated by photon–photon collisions.     

Hadron structure at small momentum transfer

Giving three examples, the form factors of the nucleon, the polarisability of the charged pion and the interference of the S₁₁(1535) with the D₁₃(1520) excitation of the nucleon in the -decay channel, it is argued that the hadron structure at low momentum transfer is highly significant for studying QCD.     

Pion production at large transverse momentum

A constituent interchange model is used to give a natural explanation of the observed energy dependence of ISR data for π° production at 90°. It is predicted that at large fixed p_T and sufficiently high energy the cross section will become constant, with a p_T dependence of (p_T²)^?2.5. It is also tentatively suggested that the e⁺e^? annihilation structure function $\text{ν}\text{W}{}_2$ should behave like ω^?1.5 near ω = 0.