On gauge invariance of Breit-Wigner propagators

We present an approach to bosonic (Z ^o,W ^±) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for theZ ^o-boson propagator we extend previous analyses and show that the part proportional tok k _v /M ² must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.     

Fermionic unparticles,gauge interactions and the <Emphasis Type="Italic">β</Emphasis> function

The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We further develop a possible gauge theory for fermionic unparticles. Computing the consequent contribution of unfermions to the β function of the theory, it is shown that this can be viewed as the sum of two contributions, one fermion-like and the other scalar-like. However, if full conformal invariance is imposed, the latter vanishes identically. We discuss the consequences thereof as well as some general phenomenological issues.     

Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Lepton flavor violating Z-boson decays induced by scalar unparticle

We predict the branching ratios of the lepton-flavor violating Z-boson decays Z→e^±μ^±, Z→e^±τ^± and Z→μ^±τ^± in the case that the lepton-flavor violation is carried by scalar unparticle mediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension, and the branching ratios can reach values of the order of 10^-8, for the heavy lepton-flavor case, for small values of the scaling dimension.     

Global study of electron–quark unparticle interactions

We perform a global fit on parity-conserving electron–quark interactions via spin-1 unparticle exchange. Besides the peculiar features of unparticle exchange due to non-integral values for the scaling dimension \(d_{\mathcal {U}}\) and a non-trivial phase factor \(\exp (-id_{\mathcal {U}}\pi)\) associated with a time-like unparticle propagator, the energy dependence of the unparticle contributions in the scattering amplitudes are also taken into account. The high energy data sets taken into consideration in our analysis are from (1) deep inelastic scattering at high Q ² from ZEUS and H1, (2) Drell–Yan production at Run II of CDF and DØ, and (3) e ⁺ e ^?→ hadrons at LEPII. The hadronic data at LEPII by itself indicated a 3–4 sigma preference of new physics over the Standard Model. However, when all data sets are combined, no preference for unparticle effects can be given. We thus deduce an improved 95% confidence level limit on the unparticle energy scale \(\varLambda_{\mathcal {U}}\).     

Scale transformations for renormalized field operators: Discussion of the soluble model

We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless λ⁴ theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure, regularization, introduction of appropriate counterterms, and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D_Λ^R(t). In the cut-off free limit Λ → ∞ the ET commutator of D_Λ^R(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory.     

Brownian Motion with Dry Friction

A small object (Solid or droplet) is placed on a horizontally vibrating plate, imposing an acceleration γ(t) in the form of a white noise. The object experiences dry friction (due to soild/solid interaction, or to contact angle hysteresis in the case of a droplet). The object is driven by a force γ(t) – Δσ(t) where σ(t), =±1, depending on the sign of the velocity. We discuss the motion at two levels: (i) in terms of simple scaling laws, (ii) by a propagator technique. (a) When Δ is below a certain crossover value Δ*, we expect an unperturbed (Langevin) Brownian motion. (b) When Δ > Δ*, we expect a reduced diffusion coefficient proportional to Δ⁻⁴ for small Δ.     

Supercurrents in color-superconducting quark matter

We review the basic properties of the currCFL-K⁰ phase in dense quark matter. At asymptotically large densities, three-flavor quark matter is in the color-flavor locked (CFL) state. The currCFL-K⁰ state is a way to respond to “stress” on the quark Cooper pairing, imposed at more moderate densities by the strange quark mass and the conditions of electric and color neutrality. We show how a kaon supercurrent is incorporated in a purely fermionic formalism, and show that the net current vanishes due to cancellation of fermion and charge-conjugate fermion contributions.     

Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999     

Gauge-invariant dressed fermion propagator in massless QED3

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED₃ is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.     

Gauge invariant green function in the Schwinger model

In two-dimensional quantum electrodynamics with massless fermions (Schwinger model), the gauge invariant one-particle fermion Green function is computed. It is shown that this Green function is independent of the choice of integration contour in the gauge exponential, and coincides with the free fermionic propagator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–52, December, 1984.The authors are deeply grateful to V. B. Belyaev and N. B. Skachkov for their stimulating interest in this work and useful comments.     

Effects of unparticles on running of gauge couplings

Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the β function a term that is (2-d) times that from a scalar particle in the same representation. This result has important implications for asymptotic freedom. An unparticle with d>2, in contrast to its matter counterpart, can speed up the approach to asymptotic freedom for a non-Abelian gauge theory and has the tendency to make an Abelian theory also asymptotically free. For not spoiling the excellent agreement of the standard model (SM) with precision tests, the infrared cut-off, m, of such an unparticle would be high but might still be reachable at colliders such as LHC and ILC. Furthermore, if the unparticle scale Λ_U is high enough, unparticles could significantly modify the unification pattern of the SM gauge couplings. For instance, with three scalar unparticles of d∼2.5 in the adjoint representation of the strong gauge group but neutral under the electroweak one, the three gauge couplings would unify at a scale of ∼ 8×10¹² GeV, which is several orders of magnitude below the supersymmetric unification scale. PACS  12.90.+b; 14.80.-j; 11.10.Hi; 12.10.Dm     

Supersymmetry and electron-hole excitations in semiconductors at finite temperature

The fermionic and bosonic electron-hole low-lying excitations in a semiconductor are analyzed at finite temperature in a unified way following Nambu's quasi-supersymmetric approach for the BCS model of superconductivity. The effective lagrangian for the fermionic modes and for the bosonic low-lying collective excitations in the semiconductor is no longer supersymmetric in a conventional finite-temperature treatment. However, the bosonic excitations do not couple directly to the heat bath and as a result, quasi-supersymmetry is restored to the effective lagrangian when a redefinition of the coupling constant associated with the collective excitations is performed. Our result shows that although the mass and coupling parameters are now temperature dependent, the fermion and boson excited states pair together and can still be transmuted into one another.     

The Landau gauge gluon propagator in lattice QCD

A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4³ × 8 lattices), β = 5.8 (400 4³ × 10 lattices and 100 6³ × 12 lattices), and β = 6.0 (100 4³ × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.     

Path integrals and linear canonical transformations

For a system withN bosonic or fermionic degrees of freedom I calculate the coherent state propagator, i.e. the matrix element between coherent states of the evolution operator, for a general quadratic Hamiltonian plus a source term, using the holomorphic form of the path integral. The analysis and the result obtained are used to discuss the transformation properties of the path integral for linear canonical transformations (Bogoliubov-Valatin trfs), a preliminary to the formulation of a geometric theory of path integral quantization.

     

Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16³ × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling α _s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling α _s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α _s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q ²) with c ≃ 2.8 GeV² on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α _s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α _s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α _s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at     

The boson-fermion hybrid representation formulation,I

A boson-fermion hybrid representation is presented. In this framework, a fermion system is described concurrently by the bosonic and the fermionic degrees of freedom. A fermion pair in this representation can be treated as a boson without violating the Pauli principle. Furthermore the “bosonic interactions” are shown to originate from the exchange processes of the fermions and can be calculated from the original fermion interactions. Both the formulation of the BFH representations for the even and odd nuclear systems are given. We find that the basic equation of the nuclear field theory (NFT) is just the usual Schrödinger equation in such a representation with the empirical NFT diagrammatic rules emerging naturally. This theory was numerically checked in the case of four nucleons moving in a single-j shell and the exactness of the theory was established.