Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Rotating bodies in general relativity

Synge's approximation method is used in order to obtain the gravitational field of a massive body with an axis of symmetry around which it is rotating steadily. The method is carried out to include the second approximation. This means that terms of orderm ² are retained as significant, and there is an error of orderm ³ in the field equations,m being the mass of the body.     

Quark condensate in the nuclear matter

We calculate the quark condensate in the nuclear matter, taking into account the single-pion and two-pion exchanges between nucleons. We find the dependence of the averaged value of the quark operator¯qq on the density of the matterρ. At very low density the nonlinear terms are proportional toρ ² and increase the tendency to restoration of the chiral symmetry. At larger values of density the account of interaction inside the matter slower down the restoration of chiral symmetry compared to the gas approximation law. The leading nonlinear term in Fermi momentum power expansion becomes of the orderρ ^4/3 . The value of the condensate at the saturation value of density is obtained. The role of multinucleon effects is analyzed.     

Bootstrapping the photon

A nontechnical review is given of a topological bootstrap theory, with emphasis on theraison d'être for an electromagnetism whose fine-structure constant is of order10 ^?2.     

A discussion of the relativistic equal-time equation

Ruan Tu-nan et al. [1] have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limitM ₂→∞ in the ladder approximation of single photon exchange. We show that up to orderO(α⁴) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of orderO(α⁶).     

On the low-temperature behavior of condensed Bose systems

A microscopic derivation of theT ²-law for the low-temperature behavior of the condensate depletion in an interacting Bose liquid is given using the knownT=0 low-lying single-particle excitations. TheT ²-term gives no contribution to the orderT ³ in the microscopic proof of Landau'sT ³-law for the specific heat of an interacting Bose liquid.     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

Recoil corrections to the hyperfine splitting of exotic atoms

All recoil corrections to the hyperfine structure to orderα ⁴ are given, for arbitrary nuclear spins.     

Resolving the on- and off-shell ambiguity of perturbative QCD using sum rules

The orderg ^?2 coefficient functions for hard processese ⁺ e ^?→hX andlh→l′ h′ X are calculated in perturbative QCD. On- and off-shell regularization of the mass singularities leads to different results. Sum rules of energy and quantum number conservation are satisfied when using the on-shell regularization and force us to reject the result of the conventional off-shell regularization.     

Exchange effect on the electronic specific heat

By improving the evaluation of the contribution from the first order exchange graphs reported recently by Tsai and Isihara, the electronic specific heat of an electron gas is evaluated to ordere ². It is shown that the specific heat contains a logarithmic term.     

The lack ofO(A −1)-contributions in the Iwamoto-Yamada-expansion of the energy expectation value per particle for extended Fermi systems

It is shown that the Iwamoto-Yamada expansion of the energy expectation value per particle of a Fermi system does not contain contributions of the orderO(A ^–1). The consequences which can be drawn are very fundamental for the radial distribution function and the liquid structure function.     

The thermodynamics of quark-gluon plasmas in external gluomagnetic fields

The external in-homogeneous gluomagnetic field contribution to the partition function is calculated in the one-loop approximation up to terms of orderG ³ for the external field. Numerically, the effect appears to be very small.     

Finite temperature effective potential for the abelian Higgs model to the ordere 4,λ 2

A complete calculation of the finite temperature effective potential for the abelian Higgs model to the ordere ⁴, λ² is presented and the result is expressed in terms of physical parameters defined at zero temperature. The absence of a linear term is verified explicitly to the given order and proven to survive to all orders. The first order phase transition has weakened in comparison with lower order calculation, which shows up in a considerable decrease of the surface tension.     

Flow equations and the strong-coupling expansion for the Hubbard model

Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at ordert ³/U² or higher.     

Hot gluon matter in a constantA 0 background

We compute the effective action of finiteT SU(3) gauge theory in a constant diagonal background fieldA ₀(t,x)=B ₀ ³ T₃+B ₀ ⁸ T₈ in the general covariant background gauge up to terms of orderg ³.B ₀ ^3,8 shield the infrared singularities and the aim is to study whether the minimum of the effective action would determine their values dynamically. We find that the orderg ² term depends explicitly on the gauge fixing parameter ξ. Since the background field screens already at the tree diagram level the interactions of the six non-diagonal gluon fields they do not contribute to the plasmon-likeg ³ term. The two diagonal fieldsA ₀ ³ ,A ₀ ⁸ do, but the electric mass squared they develop will become negative if the background fields are larger than aboutT/g. Hence large background fields make the system unstable.     

Fermion mass hierarchy based onN=8 supergravity

A possible mechanism is proposed to realize fermion mass hierarchy based on the superunification model of Ellis et al. In addition to the usual fermion (F)—Higgs (B) coupling, “non-renormalizable” interactions such as(1/(M _p ) ⁿ )(F) ² (B) ⁿ⁺¹ are introduced. It is assumed that three kinds of Higgs scalars respectively develop v.e.v. of orderM _P ,M _X andM _W , corresponding to the symmetry breaking pattern ofSU(8)→SU(5)→SU(3)×SU(3)×U(1)→SU(3)×U(1). As a result, fermions acquire their masses of orderM _w ,M _W (M _X /M _P) andM _W (M _X /M _P )². An example of the model is presented which shows nice feature of hierarchical mass patterns.