Vacuum energy in the bag model

The vacuum energy of the Yang-Mills field is examined for the conditions of the bag model. The dominance of high-frequency effects results in a vacuum energy that decomposes naturally into a volume energy, a surface energy, and higher shape energies. These quantities are identified with the parameters of the bag model. The imposition of confining boundary conditions for all frequencies is shown to be inconsistent since this would result in the bag constant and certain of the shape tensions being infinite. The manner in which the boundary conditions should be relaxed at high frequency is discussed. The most naive procedure for relaxing the boundary conditions, which is to apply confining conditions only on modes of frequency less than some cutoff frequency, results in a negative bag constant and surface tension and would render the vacuum unstable against the spontaneous breaking of Poincaré invariance. Consideration of the manner by which the interacting electromagnetic field avoids a similar instability suggests that a more realistic way to relax the boundary conditions on the bag surface is to endow the vacuum exterior to the bag with a frequency-dependent dielectric constant and magnetic permeability. In this picture the stability of the vacuum is restored, the surface tension is finite and positive, and the bag constant is zero at least to lowest order in the coupling. It is pointed out that the fermion contributions to the bag constant and the surface tension may relate to the spontaneous breaking of chiral invariance. The aim throughout is to examine the bag model, as it relates to vacuum energy, strictly in its own terms with an emphasis on questions of principle.All too often is heard the alibi that since the theory itself is only approximate, the mathematics need be no better. In truth the opposite follows. Granted that the model represents but a part of nature, we are to find what such an ideal picture implies, a result strictly derived serves to test the model; a false result proves nothing but the failure of the theorist. To call an error by a sweeter name does not correct it. The oversimplification or extension afforded by the model is not error: the model, if well made, shows at least how the universe might behave, but logical errors bring us no closer to the reality of any universe. (Truesdell and Toupin 1960).     

Finite Temperature Dimensional Regularization to Three-Loop Vacuum Graphs of Massless QED in Arbitrary Gauge

The dimensional regularization is applied to three-loop vacuum graphs in massless QED to evaluate temperature-dependent ultraviolet divergences and infrared divergences in arbitrary covariant gauge. They both are shown to be absent due to cancellations among themselves, and the cancellations are gauge-independent although the individual divergences are gauge-dependent.     

QMC模型的介质相关参数的确定及核物质中的夸克凝聚

通过把QMC模型参数展到σ场的一阶项来引入模型参数的核介质效应,并利用核子袋在介质中的平衡条件自洽地确定展开系数.计算结果表明袋参数及核子半径受介质影响较大,而零点运动参数则保持不变.在此基础上,分析了介质相关的模型参数对核物质状态方程及夸克凝聚的影响.     

The fermion vacuum in the (1+1)-dimensional chiral bag

The fermionic vacuum of the (1+1)-dimensional chiral bag of Zahed is examined in a time-dependent, adiabatic approximation. It is shown that the adiabatic vacuum gives rise to an oscillating boson field at the bag surface, whose excitation energies are in the same range as those of the valence quarks.     

The quark bag model

The quark bag model is reviewed here with particular emphasis on spectroscopic applications and the discussion of exotic objects as baryonium, gluonium, and the quark phase of matter. The physical vacuum is pictured in the model as a two-phase medium. In normal phase of the vacuum, outside hadrons, the propagation of quark and gluon fields is forbidden. When small bubbles in a second phase are created in the medium of the normal phase with a characteristic size of one fermi, the hadron constituent fields may propagate inside the bubbles in normal manner. The bubble (bag) is stabilized against the pressure of the confined hadron constituent fields by vacuum pressure and surface tension. Inside the bag the colored quarks and gluons are governed by the equations of quantum chromodynamics.     

Breathing motion of a kink-bag system in (1 + 1) dimensions: Inertia of the vacuum confined in a bag

We examine the breathing motion of a (1 + 1)-dimensional hybrid bag where the confined quarks are coupled with a solitonic chiral field at the bag boundary. The hybrid bag is a toy model for the (1 + 3)-dimensional skyrmion-bag system and its breathing motion has close connection with the excited states of a nucleon such as the Roper resonance. The collective lagrangian for the motion is derived microscopically by focusing on the polarized Dirac sea inside the bag. The mass parameter of the motion is decreased compared with the MIT-bag one owing to the negative contribution from the inertia of the confined vacuum. As a result, the spectra of the motion do not have too low excitation energies despite that the potential energy surface is softened by the vacuum effect.     

Medium dependence of the bag constant in the quark-meson coupling model

Possible variations of the quark-meson coupling (QMC) model are examined in which the bag constant decreases in the nuclear medium. The reduction is supposed to depend on either the mean scalar field or the effective mass of the nucleon. It is shown that the electric and magnetic radii of the bound nucleon are almost linearly correlated with the bag constant. Using the fact that the size of the bound nucleon inside a nucleus is strongly constrained by y-scaling data in quasi-elastic, electron-nucleus scattering, we set a limit for the reduction allowed in the bag constant for these two models. The present study implies that the bag constant can decrease up to 10–17% at average nuclear density, depending on the details of the model.     

Influences of the bag constant on properties of hybrid stars

Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 Mo (M<,⊙> is solar mass) to 1.63M<,⊙> and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant (B<'1/4>) is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.     

Thermodynamics of strange quark matter with the density-dependent bag constant

The thermodynamics of strange quark matter with density dependent bag constant are studied self-consistently in the framework of the general ensemble theory and the MIT bag model.In our treatment,an additional term is found in the expression of pressure.With the additional term,the zero pressure locates exactly at the lowest energy state,indicating that our treatment is a self-consistently thermodynamic treatment.The self-consistent equations of state of strange quark matter in both the normal and color-fla...     

ac Stark effect for a two-level atom in a squeezed vacuum via a two-photon process

The nondegenerate two-photon interaction of a two-level atom with a broadband multimode squeezed vacuum is investigated. We find that in the two-photon process the squeezed vacuum has a driving effect on the atom which can lead to an ac Stark effect when the average photon number of the squeezed vacuum is larger than a critical value. Received: 2 February 1999 / Received in final form: 20 April 1999     

On the instanton-induced portion of the nucleon strangeness II: the MIT model beyond the linearized approximation

If instantons are introduced into the MIT bag model in such a way that the bag radii are allowed to vary, the MIT bag interior can accommodate an instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the non-perturbative QCD vacuum). The instanton contribution to the baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model radii (which is associated with the increase of the instanton density) is very favorable from the standpoint of nuclear physics. Received: 7 February 2003 / Revised version: 1 April 2003 / Published online: 23 May 2003 RID="a" ID="a" e-mail: klabucar@phy.hr RID="b" ID="b" e-mail: kkumer@phy.hr RID="c" ID="c" e-mail: dmekter@rudjer.irb.hr RID="d" ID="d" e-mail: bp@phy.hr. Present address: Faculty of Civil Engineering, University of Rijeka, HR-51000 Rijeka, Croatia     

Influences of the bag constant on properties of hybrid stars

Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 M_⊙ (M_⊙ is solar mass) to 1.63 M_⊙ and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant (B^1/4) is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.     

The fuzzy bag and baryonic properties with center of mass and recoil corrections

The fuzzy bag is a hadronic model which has features both of the bag model (energy-momentum conservation, QCD vacuum energy) and of relativistic potential models (confinement achieved through a potential). It is also a chiral model, with the unique property that the pion field is suppressed in the interior of the bag by means of a scalar potential, and yet chiral symmetry is preserved. This scalar potential allows one to control how far the pion field can penetrate in the interior of the bag. We calculate the masses of the fundamental baryon octet taking into account the center of mass, one-gluon exchange and one-pion exchange corrections. We also calculate the nucleon axial charge, charge radii and magnetic moments including center of mass and recoil corrections. The agreement with experiment is excellent, and the results indicate that the pion field is suppressed only very close to the center of the bag. Received: 14 January 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: pilotto@if.ufrgs.br     

On the instanton-induced portion of the nucleon strangeness

We calculate the instanton contribution to the proton strangeness in an MIT bag enriched by the presence of a dilute instanton liquid. The evaluation is based on the expression of the nucleon matrix elements of bilinear strange-quark operators in terms of a model valence nucleon state and the interactions producing quark–antiquark fluctuations on top of that valence state. Our method combines use of the the evolution operator containing a strangeness source and the Feynman–Hellmann theorem. It enables one to evaluate the strangeness in different Lorentz channels in essentially the same way. Only the scalar channel is found to be affected by the interaction induced by the random instanton liquid. Received: 12 February 1999 / Published online: 30 June 1999     

SUSY variants of the electroweak phase transition

The MSSM with a light right-handed stop and supersymmetric models with a singlet whose vev is comparable to that of the Higgs allow for a strongly first-order electroweak phase transition even for a mass of the lightest Higgs around 100 GeV. After a short review of the standard model situation we discuss these supersymmetric models. We also compare perturbative calculations based on the dimensionally reduced 3-dimensional action with lattice results and present an analytic procedure based on an analogue of the stochastic vacuum model of QCD to estimate the nonperturbative contributions. Received: 26 September 1998 / Revised version: 2 June 1999 / Published online: 15 July 1999     

Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

Massive gauge field in source theory. II

In an earlier source theory investigation it was shown that the vacuum polarization of a massive gauge field is finite, provided that the conservation of current is imposed everywhere, including the interior of the sources. It is shown in the present paper that radiative corrections to a vertex function (two-particle production by an external source) are also finite if the same requirement about current conservation is imposed. In other words one-loop corrections turn out to be finite in both calculations. The cancellations leading to convergence may be understood in terms of Ward identities. The three form factors that appear are not only shown to be finite but are also explicity found.     

The nucleon as a topological chiral soliton

We consider a version of the chiral bag model in which the interior quark sector is joined to an exterior meson sector through the requirement of continuity of the axial vector current at the bag surface. The negative energy quark sea plays a crucial role in this model, which reduces to the Skyrme soliton in the limit as the bag radius R→0. The “leakage” of baryon number and energy through the bag results in a remarkable insensitivity of these quantities to the bag radius. Although low-energy phenomenology should display a similar insensitivity, we suggest that a bag radius of 0.44 fm is advantageous on technical grounds. This choice of R should minimize the importance of gluon corrections, vacuum fluctuation effects, and inherent uncertainties in the effective lagrangian.     

Large numbers hypothesis. IV. The cosmological constant and quantum physics

In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.