Comment on real-time finite-temperature gauge field propagators

The gauge-fixing terms of the free, real-time thermal gauge field propagators corresponding to quantization in a covariant gauge obtained by Kobes, Semenoff, and Weiss are shown to be incorrect, apart from well-known signature ambiguities in the off-diagonal elements, and to differ from those obtained by Landsman using the method of the Klein-Gordon divisor. We obtain the correct forms which are then shown to coincide with Landsman's results by means of a distributional identity.     

Particles and propagators in relativistic thermo field theory

Based on a new spectral representation of thermal correlation functions, a general characterization of stable particles in relativistic thermo field theory is given. Such particles manifest themselves by specific discrete contributions in the spectral functions and can thus be identified unambiguously.     

Analyticity of effective coupling and propagators in massless models of quantum field theory

For massless models of quantum field theory, some general theorems are proved concerning the analytic continuation of the renormalization group functions as well as the effective coupling and the propagators. Starting points are analytic properties of the effective coupling and the propagators in the momentum variablek ², which can be converted into analyticity of - and -functions in the coupling parameter . It is shown that the -function can have branch point singularities related to stationary points of the effective coupling as a function ofk ². The type of these singularities of () can be determined explicitly. Examples of possible physical interest are extremal values of the effective coupling at space-like points in the momentum variable, as well as complex conjugate stationary points close to the realk ²-axis. The latter may be related to the sudden transition between weak and strong coupling regimes in quantum chromodynamics. Finally, for the effective coupling and for the propagators, the analytic continuation in both variablesk ² and is discussed.On leave from the Max-Planck-Institut für Physik und Astrophysik, D-8000 München, Federal Republic of Germany     

Thermalization in one- plus two-body ensembles for dense interacting boson systems

Employing one- plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λ   for a system with 10 bosons (m=10$m=10$) in five single-particle levels (N=5$N=5$). It is found that in a region λ∼_λt$\lambda \sim {\lambda }_t$, different definitions give essentially the same values for temperature and entropy, thus defining a thermalization region. Also, (m,N)$(m,N)$ dependence of _λt${\lambda }_t$ has been derived. It is seen that _λt${\lambda }_t$ is much larger than the λ values where level fluctuations change from Poisson to GOE and strength functions change from Breit–Wigner to Gaussian.     

Isolated one particle states in boson quantum field theory models

We give sufficient conditions to ensure the existence of isolated one-particle states in the joint energy-momentum spectrum of an Osterwalder-Schrader scalar boson quantum field theory. We do not require the existence of sharp-time fields or weak coupling.     

Exact conditions in finite-temperature density-functional theory

Density-functional theory (DFT) for electrons at finite temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite temperature, including the adiabatic connection formula. We discuss consequences for functional construction.     

Thermalization of strongly coupled field theories

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.     

Perturbation theory with band-matrix propagators

A new version of the Rayleigh-Schrödinger type of perturbation theory is presented. It is based on a rearrangement of hamiltonians H=T+λV containing a non-diagonal (band-matrix, strong-coupling) zero-order component T. Its efficiency is illustrated on the anharmonic oscillator.     

Short distance propagators in a background field

We derive an operator expansion of the scalar, the spinor and the vector propagators in the presence of an arbitrary long range background field, using the Schwinger-DeWitt ‘proper time’ formalism. This has the advantage of keeping the expansion gauge covariant at all stages. These results may be used to calculate the leading background effects in the one-loop correlation functions.     

Thermodynamic calculations in relativistic finite-temperature quantum field theories

A Minkowski space formalism of finite-temperature quantum field theory is used to compute static thermodynamic quantities in the one- and two-loop approximation in an elegant and straightforward way using a generalization of Weinberg's tadpole method of calculating effective potentials. Systematic diagrammatic techniques for low- and high-temperature expansions are developed. Renormalizability by zero-temperature symmetric counterterms is proven for all orders in the loop expansion and demonstrated explicitly to two loops. Many useful computational techniques applicable to general finite temperature calculations are explained.     

Slave boson mean field theory for the 2-D Peierls-Hubbard system

Adapting the Kotliar-Ruckenstein slave boson approach to the Hubbard model with an additional local electronphonon interaction, we have studied the stability of the ground state against (, ) and (, 0) Peierls distortions on a square lattice. The theory is evaluated within an adiabatic two-sublattice saddle-point approximation restricted to symmetry broken states compatible with the underlying bipartite lattice, i.e. para-, ferro-, ferri- and antiferromagnetic states with and without static lattice displacement. At half-filling the Holstein coupling leads to a stable paramagnetic phase with an on-site frozen in breathing mode accompanied by a long-range charge density wave below a critical Hubbard interactionU. Away from half-filling, we distinguish between two possible phase diagrams of the Peierls-Hubbard model. One of them is obtained in the usual way of comparing the relative stability of several homogeneous phases, the other more complete one allows for heterogeneous mixing of phases. In this case we found phase separated regions with an without dimerization, homogeneous dimerized para- and ferrimagnetic states, and the pure para-and ferromagnetic phases. Upon doping the local electron-phonon coupling can induce a magnetic ordered state.     

Finite width in out-of-equilibrium propagators and kinetic theory

We derive solutions to the Schwinger–Dyson equations on the Closed-Time-Path for a scalar field in the limit where backreaction is neglected. In Wigner space, the two-point Wightman functions have the curious property that the equilibrium component has a finite width, while the out-of equilibrium component has zero width. This feature is confirmed in a numerical simulation for scalar field theory with quartic interactions. When substituting these solutions into the collision term, we observe that an expansion including terms of all orders in gradients leads to an effective finite-width. Besides, we observe no breakdown of perturbation theory, that is sometimes associated with pinch singularities. The effective width is identical with the width of the equilibrium component. Therefore, reconciliation between the zero-width behaviour and the usual notion in kinetic theory, that the out-of-equilibrium contributions have a finite width as well, is achieved. This result may also be viewed as a generalisation of the fluctuation–dissipation relation to out-of-equilibrium systems with negligible backreaction.     

Hedgehog loops and finite-temperature transition in Yang-Mills theory

Physics of Atomic Nuclei - The dynamics of non-Abelian gauge theory can be described not only in terms of local gauge fields but also in terms of nonlocal gauge-invariant variables known as Wilson...     

A theory of finite-temperature Bose-Einstein condensates in neutron stars

We investigate the possible occurrence of a Bose-Einstein condensed phase of matter within neutron stars due to the formation of Cooper pairs among the superfluid neutrons. To this end we study the condensation of bosonic particles under the influence of both a short-range contact and a long-range gravitational interaction in the framework of a Hartree-Fock theory. We consider a finite-temperature scenario, generalizing existing approaches, and derive macroscopic and astrophysically relevant quantities like a mass limit for neutron stars.     

Renormalization of the Higgs model: Minimizers,propagators and the stability of mean field theory

We study the effective actionsS ^(k) obtained byk iterations of a renormalization transformation of the U(1) Higgs model ind=2 or 3 spacetime dimensions. We identify a quadratic approximationS _Q ^(k) toS ^(k) which we call mean field theory, and which will serve as the starting point for a convergent expansion of the Green's functions, uniformly in the lattice spacing. Here we show how the approximationsS _Q ^(k) arise and how to handle gauge fixing, necessary for the analysis of the continuum limit. We also establish stability bounds onS _Q ^(k) , uniformly ink. This is an essential step toward proving the existence of a gap in the mass spectrum and exponential decay of gauge invariant correlations.Dedicated to the memory of Kurt SymanzikSupported in part by the National Science Foundation under Grant PHY 82-03669