High temperature gluon matter in the background gauge

The polarisation tensor of gluons in high temperature QCD matter is discussed in the back-ground gauge and compared with that in the temporal axialA ₀=0 gauge. In both of these the gluon polarisation tensor alone is sufficient to give the asymptotically free sign of the QCD beta function. In the former the beta function and the imaginary part of the polarisation tensor are coupled in such a way that asymptotic freedom implies instability of plasma oscillations. In the latter, due to the non-covariance of the gauge condition, the beta function and the imaginary part are decoupled in such a way that the sign of the imaginary part corresponds to stable plasma oscillations.     

Behaviour of gluons at high temperature

The screening of colour electric and magnetic fields and plasma oscillations in a high-temperature gluon plasma are investigated using linear response theory and self-consistent nonperturbative solutions to the Schwinger-Dyson equation. Static electric fields are screened, with

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. This result is proven to be gauge invariant in two ways: by computing π₀₀ in temporal axial, Coulomb and covariant gauges, and by computing the physical free energy of a heavy quark pair in the plasma in temporal axial gauge. To order g³ static magnetic fields are not screened.     

Gauge parameter dependence in the background field gauge and the construction of an invariant charge

By using the enlarged BRS transformations we control the gauge parameter dependence of Green functions in the background field gauge. We show that it is unavoidable — also if we consider the local Ward identity — to introduce the normalization value ξ₀ of the gauge parameter ξ. The dependence of Green functions on ξ₀ is governed by a partial differential equation in a similar manner as the dependence on the normalization point κ is governed by the RG equation. By modifying the Ward identity we are able to construct in 1-loop order a gauge parameter independent combination of 2-point vector and background vector functions. By explicit construction of the next orders we show that this combination can be used to construct a gauge parameter independent RG-invariant charge. However, it is seen that this RG-invariant charge does not satisfy the differential equation of the normalization value ξ₀ of the gauge parameter, and, hence, is not ξ₀-independent as required.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

Two-loop free energy for finite temperatureSU(3) gauge theory in a constant external field

A two-loop calculation of the free energy for finite temperatureSU(3) gauge theory in an external fieldA ₀=const is carried out using background Feynman gauge. Nontrivial minima of the free energy are obtained atA ₀{gT forg→0 corresponding to the gauge symmetry breakingSU(3)→U(1)×U(1). Higher order perturbative effects are briefly discussed.     

A quasi-temporal gauge

We prove that a complete fixing of the temporal gauge,A _o =0, in which one imposesa subsidiary gauge condition, such as, for instance ?_i A _i (x,t ₀) = 0 leads to consistent formulation of the theory with simple Feynman rulesand a well defined gluon propagator. The correct exponentiation of the time dependence of the Wilson loop has been checked to occur up to order g⁴.     

O(5)×U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL _L ^T (v _e ,e,,v ) _L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ?⁰_n> ?⁰_p, ?⁰ = ?⁰_n+?⁰_p = 0.17 nucleons/fm³) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for (?⁰_n??⁰_p)/?⁰ > 0.63 both zero sound and isospin sound are strongly damped.     

Vacuum copies and perturbation theory in the 't hooft-veltman gauge of QED

The 't Hooft-Veltman gauge condition ?_μA_μ + A_μ² = 0 gives a version of quantum electrodynamics with many similarities to Yang-Mills theory, including the presence of Gribov gauge-fixing ambiguities. We exhibit and discuss some properties of a family of copies of the vacuum, emphasizing their bearing on perturbation theory and the choice of a vacuum state. It is shown that in a general gauge theory, the same perturbation series results from expanding about any gauge-copy of the vacuum.     

Seiberg-Witten geometry with various matter contents

We obtain the Seiberg-Witten geometry for four-dimensional N = 2 gauge theory with gauge group SO(2N_c) (N_c ⩽ 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N = 2 E₆ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N = 2 SU(N_c) (N_c ⩽ 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N = 1 confining phase superpotentials.     

Quantization of gauge-fields in the fock-schwinger gauge

The gauge conditionx _μ A ^μ =0 produces a theory which is free from Faddeev-Popov ghosts, but whose Green's functions obviously lack translational invariance. We present for the first time a consistent perturbation theory in this gauge. Besdes discussing example howlocal counter-terms in the action suffice for the one-loop renormalization ofS-matrix elements.     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

Renormalization constants in asymptotically free field theories

Renormalization constants Z_i for asymptotically free field theories can be computed via renormalization group techniques from perturbation theory. We show that there exists a subclass of these theories in which, by virtue of a new eigenvalue condition on the gauge parameter, the Z_i are asymptotically gauge independent, and hence can vanish in all gauges.     

Decay instability of plasma in crossed fields

In this paper it is shown that in plasma placed in crossed electric and magnetic fields, oscillations are excited with the frequency close to the drift frequencyω ₀ =k _? υ _? . Decay of the oscillations into two other oscillations, for which the selection rulesω ₀ =ω ₂ ?ω ₁ andm ₀=m ₂?m ₁ hold, where the frequencyω ₁ is close to the Langmuir frequency of ions, was observed.     

Universal properties of U(1) gauge theories

The previously known analogies between four-dimensional compact U(1) lattice gauge theories and the two-dimensional planar model are extended to a number of other results. We show that the monopoles in the gauge theory renormalize the coupling constant α by an amount proportional to the susceptibility of the monopole gas. Confinement occurs when this susceptibility diverges. We argue that α is analogous to the critical exponent η of the planar model, and that the transition occurs at a universal critical value α_c.We also define an analogue of the superfluid density for the gauge theory, in terms of the dependence of the free energy on the boundary conditions, and show that it is universally related to α. Finally, we show that the same physics emerges from a continuum U(1) theory with real magnetic monopoles.     

Invariants for E0-Semigroups on II1 Factors

We introduce four new cocycle conjugacy invariants for E ₀-semigroups on II ₁ factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow. Using noncommutative Itô integrals we show that the dimension of the gauge group can be computed from the structure of the additive cocycles. We do this for the Clifford flows and even Clifford flows on the hyperfinite II ₁ factor, and for the free flows on the free group factor ${L(F_\infty)}$ L ( F ∞ ) . In all cases the index is 0, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the C*-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate E ₀-semigroups.     

The structure of Yang-Mills theories in the temporal gauge: (II). Perturbation theory

In this paper we construct the perturbative expansion for the Feynman propagation kernel of a Yang-Mills theory in the A₀ = 0 gauge in any external charge sector, by using the expression of the kernel derived in a previous paper. Unlike the usual one, in this formulation of perturbation theory there are no spurious poles at zero energy transfer in the (effective) gauge field propagator. Examples of calculations of the static potential between external (infinitely heavy) non-abelian charges and of scattering amplitudes are discussed in detail.