Finite temperature Cornwall-Jackiw-Tomboulis formalism of Φ6 theory

The finite temperature effective potential for a scalar field with Φ⁶ interaction is calculated by extending the CJT formalism for composite operators. It is found that unrenormalized terms appear in the effective potential due to the presence of an unrenormalized mass term. Nonzero turning points are obtained both for positive and negativeλ. High temperature expansion is performed and the results are analysed numerically. Graphical analysis indicates symmetry restoration whenT→0.     

Symmetry-improved CJT effective action

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2)$\mathbb{O}(2)$ scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2)$\mathbb{O}(2)$ is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.     

Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Thermodynamical consistent CJT calculation in studying nuclear matter

We have attempted to apply the CJT formalism to study the nuclear matter. The thermodynamic potential is calculated in Hartree–Fock approximation in the CJT formalism. In the calculation, as the first step, we have neglected the medium effects to the mesons, the momentum dependence in the nucleon self-energy and the fluctuations of the vacuum. After these approximations, the numerical results are found very consistent with those obtained from the mean field calculation. In our calculation the thermodynamical consistency is also preserved.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Effective Field Theory for Fermi Systems in a Large N Expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where N is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.     

Higher derivative correction to Kaluza–Klein black hole solution

We investigate the attractor mechanism in a Kaluza–Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as the entropy function formalism. We consider different higher derivative terms with a general coupling to the moduli field. For the R ² theory, we use an effective potential approach, looking for solutions which are analytic near the horizon and showing that they exist and enjoy attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of R ⁿ terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza–Klein black hole solution we show that a higher derivative correction dresses the singularity for an appropriate coupling, and we can find the attractor solution.     

Band parameters for cadmium and zinc chalcogenide compounds

Theoretical investigations of the electronic, optical and elastic properties of cadmium and zinc chalcogenides in the zinc-blende structure are performed using a pseudopotential formalism. Our results are in reasonable agreement with the available experimental data. Polynomial expressions are obtained for the electron effective mass and the static dielectric constant as a function of the fundamental energy band-gap. Relations of elastic constants ratio to the ionicity are also examined and discussed.