scholarly journals BAGS AND CONFINEMENT GOVERNED BY SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

2010 ◽  
Vol 25 (22) ◽  
pp. 4195-4220 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Energy Density ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Field ◽  
Scale Invariance ◽  
Vacuum Energy ◽  
Equations Of Motion ◽  
Flat Space ◽  
Vacuum Energy Density ◽  
Conformally Invariant

A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard [Formula: see text] where g is the determinant of the metric and another measure Φ independent of the metric. To implement scale invariance, a dilaton field is introduced. Using the first-order formalism, curvature (ΦR and [Formula: see text]) terms, gauge field term ([Formula: see text] and [Formula: see text]) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well-defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is nonconfining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.

TWO MEASURES THEORY APPROACH TO BAGS AND CONFINEMENT

2011 ◽  
Vol 20 (supp01) ◽  
pp. 237-244
Author(s):  
EDUARDO I. GUENDELMAN
Keyword(s):  
Gauge Field ◽  
Scale Invariance ◽  
Equations Of Motion ◽  
Flat Space ◽  
Global Scale ◽  
Vacuum Energy Density ◽  
Theory Approach ◽  
Conformally Invariant ◽  
Space Limit ◽  
Two Measures

We consider the question of bags and confinement in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density. For scale invariance a dilaton field Φ is considered. Using the first order formalism, curvature (ΦR and [Formula: see text]) terms, gauge field term ([Formula: see text] and [Formula: see text]) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags the gauge dynamics is normal, that is non confining, while for the outside, the gauge field dynamics is confining.

scholarly journals NONSINGULAR ORIGIN OF THE UNIVERSE AND ITS PRESENT VACUUM ENERGY DENSITY

2011 ◽  
Vol 26 (17) ◽  
pp. 2951-2972 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Energy Density ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Scale Invariance ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Emergent Universe ◽  
Present Universe ◽  
The Universe ◽  
Origin Of The Universe

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking of scale invariance. After spontaneous symmetry breaking of scale invariance it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → - ∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → - ∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

scholarly journals CONNECTING THE NONSINGULAR ORIGIN OF THE UNIVERSE, THE VACUUM STRUCTURE AND THE COSMOLOGICAL CONSTANT PROBLEM

2013 ◽  
Vol 22 (09) ◽  
pp. 1330018 ◽  
Author(s):  
EDUARDO I. GUENDELMAN ◽  
PEDRO LABRAÑA
Keyword(s):  
Energy Density ◽  
Scale Invariance ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Emergent Universe ◽  
Vacuum Structure ◽  
Inflationary Phase ◽  
Present Universe ◽  
The Universe ◽  
Origin Of The Universe

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → -∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The nontrivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

CONFINEMENT EFFECT AS A RESULT OF SPONTANEOUS BREAKING OF SCALE INVARIANCE

2009 ◽  
Vol 24 (07) ◽  
pp. 1443-1456 ◽  
Author(s):  
I. KOROVER ◽  
E. I. GUENDELMAN
Keyword(s):  
Potential Energy ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Scale Invariance ◽  
Critical Size ◽  
Opposite Sign ◽  
Equations Of Motion ◽  
Point Of View ◽  
Spontaneous Breaking ◽  
Neutral System

In this paper the consequences of introducing spontaneous symmetry breaking of scale invariance through a scale that is obtained from the integration of the equations of motion of four index field strengths are studied. Confinement is obtained for all values of this constant of integration. For negative values two point charges have a potential energy that grows linearly with distance, but they can be arbitrarily far apart (although this is costly from the point of view of energy). For positive values of the integration constant, there is no possibility of separating charges too far apart; at a certain point a new charge of opposite sign has to be added to form a neutral system that cannot be bigger that a critical size. We discuss this using different methods, including some developed by Adler and Piran. In addition, we discuss a few alternative effective actions that are similar and that also give confinement.

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.

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