Scalar Tachyons in the de Sitter Universe

We provide a construction of a class of local and de Sitter covariant tachyonic quantum fields which exist for discrete negative values of the squared mass parameter and which have no Minkowskian counterpart. These quantum fields satisfy an anomalous non-homogeneous Klein–Gordon equation. The anomaly is a covariant field which can be used to select the physical subspace (of finite co-dimension) where the homogeneous tachyonic field equation holds in the usual form. We show that the model is local and de Sitter invariant on the physical space. Our construction also sheds new light on the massless minimally coupled field, which is a special instance of it.     

Isolating vacuum amplitudes in quantum field calculations at finite temperature

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. However, at least with the regularization used in this paper, this simple analytical structure does not hold for arbitrary diagrams, as revealed by counter-examples. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture for a relation, in the imaginary time formalism, between the expressions of a Feynman diagram at zero and finite temperature.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.     

q-deformed supersymmetric Newton oscillators

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at is shown to be supported by finite temperature lattice calculations. Received: 27 September 2000 / Published online: 8 December 2000     

Nontopological finite temperature induced fermion number

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite T induced fermion number is temperature dependent but topological.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

The potential of effective field theory in NN scattering

We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range — which occurs in nature — requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_π). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.     

Transitions to the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in two dimensions

We explore the nature of the transition to the Fulde-Ferrell-Larkin- Ovchinnikov superfluid phases in the low temperature range in two dimensions, for the simplest isotropic BCS model. This is done by applying the Larkin-Ovchinnikov approach to this second order transition. We show that there is a succession of transitions toward ever more complex order parameters when the temperature goes to zero. This gives rise to a cascade with, in principle, an infinite number of transitions. Except for one case, the order parameter at the transition is a real superposition of cosines with equal weights. The directions of these wavevectors are equally spaced angularly, with a spacing which goes to zero when the temperature goes to zero. This singular behaviour in this T = 0 limit is deeply linked to the two-dimensional nature of the problem.     

Design of an optimal wave-vector filter for enhancing the resolution of reconstructed source field by near-field acoustical holography (NAH)

In near-field acoustical holography using the boundary element method, the reconstructed field often diverges due to the presence of small measurement errors. In order to handle this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the determination of an optimal truncation order is difficult. In this article, an iterative inverse solution technique is suggested in which the mean-square error prediction is used. A statistical estimation of the minimum mean-square error between measured pressures and the model solution is required for yielding the optimal number of iterations. The continuous curve of an optimal wave-vector filter is designed, for suppressing the high-order modes that can produce large reconstruction errors. Experimental results from a baffled radiator reveal that the reconstruction errors can be reduced by this form of regularization, by at least 48% compared to those without any regularization. In comparison to results using the optimal truncation method of regularization, the new scheme is shown to give further reductions of truncation error of between 7% and 39%, for the example in this article.     

Chiral fermions in stochastic quantization

The simultaneous conservation of chiral and gauge currents in the framework of stochastic quantization is discussed. By means of the stochastic regularization procedure we explicitly compute the axial anomaly for fermions with mass m≠0 and the fictitious time t→∞. However, when m≡0, an ambiguity appears: it turns out that the two limits (m→0, t→∞) do not commute. In this case non-perturbative methods show that the difference between left-handed and right-handed zero modes cancels; therefore no anomaly is present and stochastic regularization is unable to describe chiral theories at finite fictitious time. It is in any case unclear how stochastic quantization can describe a massless fermion at finite t.     

Fractional derivative quantum fields at positive temperature

This paper considers fractional generalization of finite temperature Klein–Gordon (KG) field and vector potential in covariant gauge and static temporal gauge. Fractional derivative quantum field at positive temperature can be regarded as a collection of infinite number of fractional thermal oscillators. Generalized Riemann zeta function regularization and heat kernel techniques are used to obtain the high temperature expansion of free energy associated with the fractional KG field. We also show that quantization of the fractional derivative fields can be carried out by using the Parisi–Wu stochastic quantization.     

Singular critical endpoint and phase diagrams of the anisotropic 3-state Potts model on square lattice

We have studied the ground state and thermodynamic properties of the anisotropic 3-state Potts model on square lattice by means of the tensor network-based numerical method. The phase diagrams of this model in the ground state and at finite temperature are identified. The singular behavior at the critical endpoint along the phase boundary is carefully investigated. It is discovered that the sharp peaks appear in the second-order derivative of the field as well as the first-order derivative of the magnetization with respect to temperature on the phase boundary. Our numerical results confirm the prediction of Fisher et al. about the critical endpoint.     

On the chiral transition temperature in bilocal effective QCD

The breakdown of chiral symmetry in a many-quark system at finite temperature is studied by considering a bilocal quark interaction derived from a field theoretical treatment of QCD. We find that such an approach yields a chiral transition temperature which is about 30% lower compared to the standard NJL model prediction.     

Dynamics of Logamediate and Intermediate Scenarios in the Dark Energy Filled Universe

We have considered a model of two component mixture i.e., mixture of Chaplygin gas and barotropic fluid with tachyonic field. In the case, when they have no interaction then both of them retain their own properties. Let us consider an energy flow between barotropic and tachyonic fluids. In both the cases we find the exact solutions for the tachyonic field and the tachyonic potential and show that the tachyonic potential follows the asymptotic behavior. We have considered an interaction between these two fluids by introducing a coupling term. Finally, we have considered a model of three component mixture i.e., mixture of tachyonic field, Chaplygin gas and barotropic fluid with or without interaction. The coupling functions decays with time indicating a strong energy flow at the initial period and weak stable interaction at later stage. To keep the observational support of recent acceleration we have considered two particular forms (i) Logamediate Scenario and (ii) Intermediate Scenario, of evolution of the Universe. We have examined the natures of the recent developed statefinder parameters and slow-roll parameters in both scenarios with and without interactions in whole evolution of the universe.     

Landau theory of the finite temperature mott transition

In the context of the dynamical mean-field theory of the Hubbard model, we identify microscopically an order parameter for the finite temperature Mott end point. We derive a Landau functional of the order parameter. We then use the order parameter theory to elucidate the singular behavior of various physical quantities which are experimentally accessible.     

Thermodynamics of Modified Chaplygin Gas and Tachyonic Field

Here we generalize the results of the work of Myung () in modified Chaplygin gas model and tachyonic field model. Here we have studied the thermodynamical behavior and the equation of state in terms of volume and temperature for both models. We have used the solution and the corresponding equation of state of our previous work (Chattopadhyay et al., Astrophys. Space Sci. 314:41, 2008). for tachyonic field model. We have also studied the thermodynamical stability using thermal equation of state for the tachyonic field model and have shown that there is no critical points during thermodynamical expansion. The determination of T _∗ due to expansion for the tachyonic field have been discussed by assuming some initial conditions. Here, the thermal quantities have been investigated using some reduced parameters.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.