scholarly journals DIAGRAMMATIC APPROACH TO THE VACUUM ENERGY DENSITY: THE GROSS-NEVEU MODEL AT LARGE-N

1994 ◽  
Vol 09 (13) ◽  
pp. 1195-1205 ◽  
Author(s):  
HIROFUMI YAMADA
Keyword(s):  
Energy Density ◽  
Effective Charge ◽  
Vacuum Energy ◽  
Chiral Condensate ◽  
Vacuum Energy Density ◽  
Hartree Fock ◽  
Large N ◽  
Optimal Value ◽  
Exact Energy ◽  
Gross Neveu Model

An approach to the vacuum energy density based on a direct diagrammatic expansion in the generalized Hartree-Fock scheme is studied in the Gross-Neveu model as an example. To keep the coherence with the calculation of the chiral condensate, the vacuum energy density, ε, is expanded in terms of the effective charge associated with the condensate. Then ε is calculated by substituting the optimal value of the effective charge which specifies the solution for the condensate. The result agrees well with the exact energy density to several higher orders of the expansion, showing that our procedure works well.

scholarly journals A REMARK ON NONCONFORMAL NONSUPERSYMMETRIC THEORIES WITH VANISHING VACUUM ENERGY DENSITY

2001 ◽  
Vol 16 (27) ◽  
pp. 1761-1773
Author(s):  
OLINDO CORRADINI ◽  
ALBERTO IGLESIAS ◽  
ZURAB KAKUSHADZE ◽  
PETER LANGFELDER
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Energy Density ◽  
Vacuum Energy ◽  
Gauge Theories ◽  
Vacuum Energy Density ◽  
Large N

We discuss nonconformal nonsupersymmetric large-N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of type IIB D3-branes embedded in orbifolded space–times. We also discuss gravity in this setup.

CHIRAL QCD VACUUM ENERGY DENSITY IN THE ZERO MODES ENHANCEMENT QUANTUM MODEL

2000 ◽  
Vol 15 (01) ◽  
pp. 45-64 ◽  
Author(s):  
V. GOGOHIA ◽  
H. TOKI ◽  
T. SAKAI ◽  
Gy. KLUGE
Keyword(s):  
Energy Density ◽  
Vacuum Energy ◽  
Chiral Limit ◽  
Dyson Equation ◽  
Chiral Condensate ◽  
Vacuum Energy Density ◽  
Quantum Model ◽  
Yang Mills ◽  
Qcd Vacuum ◽  
Order Of Magnitude

Using the effective potential approach for composite operators we have formulated the quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative q-4-type dynamical, topologically nontrivial excitations of the gluon field configurations (due to self-interaction of the massless gluons only). The QCD vacuum is found to be stable since the vacuum energy density has no imaginary part. The Yang–Mills (YM) part of the vacuum energy density is always negative and depends on a finite scale at which nonperturbative effects become important. The quark part of the vacuum energy density depends in addition on the constant of integration of the corresponding Schwinger–Dyson equation. The value of the above-mentioned scale is determined from the bounds for the pion decay constant in the chiral limit. Our value for the chiral QCD vacuum energy density is one order of magnitude bigger than the instanton based models can provide while a fair agreement with recent phenomenological and lattice results for the chiral condensate is obtained.

scholarly journals THE GENERALIZED HARTREE-FOCK METHOD IN THE GROSS-NEVEU MODEL

1994 ◽  
Vol 09 (32) ◽  
pp. 5651-5672
Author(s):  
HIROFUMI YAMADA
Keyword(s):  
Nonperturbative Effects ◽  
Chiral Condensate ◽  
Gaussian Kernel ◽  
Fermion Mass ◽  
Coupling Constant ◽  
Hartree Fock ◽  
Large N ◽  
Effective Charges ◽  
Mass Terms ◽  
Gross Neveu Model

In the generalized Hartree-Fock scheme one can incorporate nonperturbative effects from the beginning of a diagrammatic expansion. In order to make a detailed analysis of the method, we apply it to the Gross-Neveu model as an example and calculate the chiral condensate at large N by using a direct diagrammatic expansion. The unperturbed Gaussian kernel is adjusted to be massive by adding fermion mass terms and the mass terms are subtracted from the interaction part, thus not changing the full Lagrangian. The chiral condensate <gσ> is expanded in powers of the renormalized coupling constant and then improved by the method of effective charges. We find that our diagrammatic expansion is compatible with renormalization. By using the principle of minimal sensitivity, we evaluate <gσ> and show that the exact broken and unbroken solutions for the discrete γ5 symmetry are obtained at each order of the expansion.

scholarly journals LOCAL CONTRIBUTION OF A QUANTUM CONDENSATE TO THE VACUUM ENERGY DENSITY

2003 ◽  
Vol 18 (10) ◽  
pp. 683-690 ◽  
Author(s):  
GIOVANNI MODANESE
Keyword(s):  
Energy Density ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Landau Equation ◽  
Vacuum Energy Density ◽  
Negative Effects ◽  
Ginzburg Landau ◽  
Physical Conditions ◽  
Local Contribution ◽  
Gravitational Vacuum

We evaluate the local contribution gμνL of coherent matter with Lagrangian density L to the vacuum energy density. Focusing on the case of superconductors obeying the Ginzburg–Landau equation, we express the relativistic invariant density L in terms of low-energy quantities containing the pairs density. We discuss under which physical conditions the sign of the local contribution of the collective wave function to the vacuum energy density is positive or negative. Effects of this kind can play an important role in bringing the local changes in the amplitude of gravitational vacuum fluctuations — a phenomenon reminiscent of the Casimir effect in QED.

scholarly journals Brownian motion and polarized three-dimensional quantum vacuum

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
Author(s):  
Davide Fiscaletti
Keyword(s):  
Dark Matter ◽  
Brownian Motion ◽  
Energy Density ◽  
Nonlinear Model ◽  
Vacuum Energy ◽  
Three Dimensional ◽  
Vacuum Energy Density ◽  
Quantum Vacuum ◽  
Virtual Particles ◽  
Fundamental Entity

A nonlinear model of Brownian motion is developed in a three-dimensional quantum vacuum defined by a variable quantum vacuum energy density corresponding to processes of creation/annihilation of virtual particles. In this model, the polarization of the quantum vacuum determined by a perturbative fluctuation of the quantum vacuum energy density associated with a fluctuating viscosity, which mimics the action of dark matter, emerges as the fundamental entity which generates the Brownian motion.

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