MH would like to dedicate this paper to Keitaro Nagata, who loved QCD more than anybody else does. v2: The presentation was improved. The logic and conclusion are unchanged. v3: References were added, some discussions were elaborated, typographical errors in Appenx A were fixed. v4: Matches the version accepted for publication in JHEP
We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from $N^0$ to $N^2$, which persists in the weak coupling region. Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in gauge theory, and S$_N$ permutations in the system of identical bosons -- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
Bose condensation is usually a low temperature phenomenon due to a low particle number density. When the number density is kept large compared to the inverse Compton volume, Bose condensation can occur at a temperature much higher than the mass of the particle. We can then use a three dimensional effective theory to study the thermal properties. We compute the transition temperature for a complex scalar field theory with a small interaction parameter.
We present a simple proof of the absence of Bose--Einstein condensation of a relativistic boson gas, in any finite local magnetic field in less than five dimensions. We show that the relativistic charged boson gas exhibit a genuine Meissner--Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well--known non--relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. The result is discussed in the context of kaon condensation in neutron stars.
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized $ζ$-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension $q$ associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Ei…
In this paper we study the corrections emergent from a Hořava-Lifshitz extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discussed some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations were done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtained the Lifshitz scaling correction for the critical temperature $T_c$ that sets the Bose-Einstein Condensation.
With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A $μ-T$ phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can happen either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area…
The problem of Bose-Einstein condensation for a relativistic ideal gas on a 3+1 dimensional manifold with a hyperbolic spatial part is analyzed in some detail. The critical temperature is evaluated and its dependence of curvature is pointed out.
We study the interplay of duality and confinement in certain three-dimensional models induced by the condensation of topological defects. To this end we check for the confinement phenomenon, in both sides of the duality, using the static quantum potential within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a linear term leading to the confinement of static probe charges.
Bose-Einstein condensation of charged scalar and vector particles may actually occur in presence of a constant homogeneous magnetic field, but there is no critical temperature at which condensation starts. The condensate is described by the statistical distribution. The Meissner effect is possible in the scalar, but not in the vector field case, which exhibits a ferromagnetic behavior.
In this paper we study the corrections emergent from a Lorentz-violating CPT-odd extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discussed some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations were done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtained a Lorentz-violating correction for the critical temperature $T_c$ that sets the Bose-Einstein Condensation.
We discuss the thermodynamic potential of a charged Bose gas with the chemical potential in arbitrary dimensions. The critical temperature for Bose-Einstein condensation is investigated. In the case of the compactified background metric, it is shown that the critical temperature depends on the size of the extra spaces. The asymmetry of the "Kaluza-Klein charge" is also discussed.
The behavior of a Bose-Einstein ideal gas of particles in a three dimensional space in the presence of a uniform field, such as gravity, and of contact interaction, describing the presence of one impurity, is investigated. It is shown that Bose-Einstein condensation can not occur.
We study the static quantum potential for a theory of anti-symmetric tensor fields that results from the condensation of topological defects, within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static probe charges.
We construct a partition function for fields obeying a quasiperiodic boundary condition at finite temperature, $ψ(0;\vec x)= e^{iθ} ψ(β;\vec x)$, which interpolate continously that ones corresponding to bosons and fermions and discuss the possibility of condensation for these fields.
We consider the model of self-interacting complex scalar fields with a rigid gauge invariance under an arbitrary gauge group $G$. In order to analyze the phenomenon of Bose-Einstein condensation finite temperature and the possibility of a finite background charge is included. Different approaches to derive the relevant high-temperature behaviour of the theory are presented.
We study the static quantum potential for a theory of anti-symmetric tensor fields that results from the condensation of topological defects, within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static probe charges.
We study the Bose-Einstein condensation of a gas with $SU_q(2)$ symmetry. We show, in the thermodynamic limit, that the boson interactions introduced by the quantum group symmetries enhance Bose-Einstein condensation giving a discontinuity in the heat capacity $C_v$ at the critical temperature $T_c$. The critical temperature and the gap in $C_v$ increase with the value of the parameter $q$ and become approximately constant for $q>3$.
We investigate the phenomenon of Bose-Einstein condensation on manifolds constructed as a product of a three-dimensional Euclidian space and a general smooth, compact $d$-dimensional manifold possibly with boundary. By using spectral $ζ$-function methods, we are able to explicitly provide thermodynamical quantities like the critical temperature and the specific heat when the gas of bosons is confined, in the three-dimensional manifold, by the experimentally relevant anisotropic harmonic oscillator potential.
It is shown that Bose-Einstein condensation occurs for an ideal gas in two spatial dimensions in the presence of one impurity which is described quantum mechanically in terms of a point-like vortex and a contact interaction. This model is exactly solvable and embodies as a special case the analogous problem in three spatial dimensions.
We show that Bose-Einstein condensation of charged scalar fields interacting with a topological gauge field at finite temperature is inhibited except for special values of the topological field. We also show that fermions interacting with this topological gauge field can condense for some values of the gauge field.
We compute deviations from ideal gas behavior of the pressure, density, and Bose-Einstein condensation temperature of a relativistic gas of charged scalar bosons caused by the current-current interaction induced by electromagnetic quantum fluctuations treated via scalar quantum electrodynamics. We obtain expressions for those quantities in the ultra-relativistic and nonrelativistic limits, and present numerical results for the relativistic case.
The behavior of an ideal $D$-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrarily to an old standing folklore, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\neq 0$ for $D=1,2,3$ if there is a point-like impurity at the bottom of the vessel containing the gas.
Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. In the Bose-Einstein Condensation model, dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present work, we study the Bose-Einstein Condensation process in a cosmological context, by assuming that this process can be described (at least approxima…
