Renormalized Wick expansion for a modified PQCD

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m_q and m_g associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m_q and m_g is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.     

Gauge-invariance properties and singularity cancellations in a modified PQCD

The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter α. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the α-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge-invariance properties. PACS 12.38.Aw, 12.38.Bx, 12.38.Cy, 14.65.Ha     

A path integral formula for quark condensate states in?a?modified?PQCD

A modified version of PQCD considered in previous works is investigated here in the case of retaining only the quark condensate. The Green function generating functional is expressed in a form in which Dirac’s delta functions are now absent from the free propagators. The new expansion implements the dimensional transmutation effect through a single interaction vertex in addition to the standard ones in massless QCD. The new vertex suggest a way for constructing an alternative to the SM, in which the mass and CKM matrices could be generated by the instability of massless QCD under the production of the top quark and other fermions condensates, in a kind of generalized Nambu–Jona-Lasinio mechanism. The results of a two loop evaluation of the vacuum energy indicate that the quark condensate is dynamically generated. However, the energy as a function of the condensate parameter is again unbounded from below in this approximation. Assuming the existence of a minimum of the vacuum energy at the experimental value of the top quark mass m _q =173 GeV, we evaluate the two particle propagator in the quark–anti-quark channel in zero order in the coupling and a ladder approximation in the condensate vertex. Adopting the notion from the former top quark models in which the Higgs field corresponds to the quark condensate, the results suggest that the Higgs particle could be represented by a meson which might appear at energies around twice the top quark mass.     

Effective potential in a curved space-time

A method is proposed for finding the effective potential in an external gravitational field on the basis of the equation of a renormalized group. The effective potential is found in the single-loop approximation for the scalar field theory and for the asymptotically free theory containing non-Abelian calibration fields, scalars, and spinors with an arbitrary value of the parameter of nonminimal coupling between the scalar and gravitational fields. The effect of quantum corrections on spontaneous symmetry violation is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 17–22, July, 1984.     

Effect of a modified potential barrier in field emission

The use of a modified surface potential barrier, which includes not only classical image force and the external force but also the exchange and correlation forces on the field emission has been investigated for tungsten. The theoretical calculations of the emitted current density and total energy distribution are obtained. A comparison of the experimental results with the theoretical predictions has been made. The agreement between them is good.     

Effective electron-hole potential in polar semiconductors

Summary An accurate analytic expression for the electron-hole effective potential in polar semiconductors is derived, by use of a preceding self-consistent calculation of the author. Its form relies on the main assumption that the excitonic envelope function can be of the 1s-orbital form and that the ground-state wave function is well described in its phonon part by a coherent-state shape with a phonon displacement function depending on the relative electron-hole distance. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Effective two-mode description of a few ultra-cold bosons in a double-well potential

We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more closely than the traditional two-mode model.     

Plane wave method with a modified potential field

Acta physica Academiae Scientiarum Hungaricae - A new method is developed for the determination of the energy band spectrum of metal electrons. An essential advantage of the method is that it...     

Effective potential for quantum scalar fields in a de Sitter geometry

We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.     

Effective potential for non-convex potentials

It is shown that the well-known relationship between the effective potential Γ and the vacuum graphs Σ of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields ? if, and only if, the classical potential is convex. In the non-convex case Σ appears to become complex for some values of ?, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all ?, and reduces to Σ in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive.     

Effective potential for water vapour

A suitable temperature dependence is introduced into the force parameters of the Lennard-Jones potential by taking the free-energy average of the Rowlinson potential. The resulting temperature-dependent parameters are used to calculate the effective potential, which is plotted for water vapour at a few different temperatures. The temperature-dependence of the second virial coefficient is shown for the cases of temperature-independent and temperature-dependent parameters of which the latter agrees very well with experimental results.     

Effective potential for ammonia vapour

The modified free-energy averaged potential for water vapour is extended to NH₃ vapour. The resulting temperature-dependent parameters are used to compute the second virial coefficient of NH₃ vapour which agrees with experimental results particularly at higher temperatures.     

Effective potential for three-body forces in fluids

We develop a model for an effective Axilrod–Teller–Muto (ATM) triple-dipole interaction based on accurate calculations of three-body effects on the third virial coefficient. The effective ATM interaction is written as a two-body density-dependent potential and is obtained by averaging the ATM function over the position of the third particle. It is shown that the addition of the mean ATM potential does not affect much the form of the binary interaction and so it can be incorporated as an effect on the minimum of the potential (position and depth). The underlying binary potentials are modelled by Approximate Non-Conformal (ANC) functions that have been proven to be highly accurate in accounting for effective pair interactions in many fluids of interest. The final total effective potential, binary plus ternary, is expressed in terms of the same ANC functions. The adequacy of the effective three-body force thus found is tested by looking at the pressure and specific heat of various fluids, formed by small nonpolar molecules, in the region of moderate densities where a third-virial approximation is reliable, and then comparing them against experimental results. The critical temperatures and volumes of those fluids are also calculated and the three-body effects on them are assessed.     

Effective interactions in the proton optical-model potential

A six-parameter optical model is developed in which the real central part is calculated by folding several effective nucleon-nucleon interactions into matter distributions which reproduce single-particle binding energies and electron scattering data. A simple local approximation is made to take into account the exchange term. It is concluded that the density-dependent effective interactions derived from nuclear-structure calculations are also appropriate for nucleon-nucleus scattering. Off-shell effects are apparent from the worsening of the quality of fit for light nuclei.     

Effective classical potential and particle distribution of a coulomb system

As a further test of the quality of the recently proposed method of effective classical potentials, we calculate the distribution function of a particle in a Coulomb field and compare the result with the exact distribution.