Two loop low temperature corrections to electron self energy

We recalculate the two loop corrections in the background heat bath using real time formalism. The procedure of the integrations of loop momenta with dependence on finite temperature before the momenta without it has been followed. We determine the mass and wavefunction renormalization constants in the low temperature limit of QED, for the first time with this preferred order of integrations. The correction to electron mass and spinors in this limit is important in the early universe at the time of primordial nucleosynthesis as well as in astrophysics.     

String corrections to the motion of a particle in the gravitational field of a black hole

The low-energy effective action, quadratic with respect to the Riemann tensor, of string theory is used to study the motion of a test particle in the gravitational field of a black hole.V. I. Ul'yanov-Lenin Kazan State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–85, January, 1994.     

On the interpretation of gravitational corrections to gauge couplings

Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms quadratic in the field strength but with higher-order space–time derivatives. We observe that such terms can be removed by appropriate local field redefinitions, and do not contribute to physical scattering-matrix elements. We illustrate this observation in the context of open string theory, where the effective action includes, among other terms, the well-known Born–Infeld form of non-linear electrodynamics. We conclude that the quadratically energy-dependent gravitational corrections are not physical in the sense of contributing to the running of a physically-measurable gauge coupling, or of unifying couplings as in string theory.     

Higher corrections in the theory of vacuum polarization by an isotropic gravitational field

A version of the effective Lagrangian method is proposed, which proves to be more effective than the well-known Schwinger-de Witt method for solving self-consistent problems concerning polarization of the matter field vacuum by an isotropic gravitational field. The main result of the paper is computation of polarizationinduced corrections of fourth order in space-time curvature and its derivatives, for scalar and vector massive fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 61–68, October, 1989.The authors thank K. A. Bronnikov, V. N. Lukash, V. N. Mel'nikov, V. N. Ponomarev, A. A. Starobinskii, and V. P. Frolov for many useful discussions of the results of this paper.     

Finite-size corrections to the free energy of Coulomb systems with a periodic boundary condition

Classical Coulomb systems ind dimensions (d?2) with a periodic boundary condition, periodW, in the directionx ^(d)are considered. With the other directions of the confining volume of lengthL, it is shown that if the system is in a conducting phase, then the “strip” free energykTf _W ,f _W = ?lim _L→∞ L ^?(d?1) log Z, has the large-W expansion $$f_W \sim Wf_\infty + \frac{{(d/2 - 1)\Gamma (d/2 - 1)}}{{\pi ^{d/2} W^{d - 1} }}\zeta (d) + O\left( {\frac{1}{{W^{d + 1} }}} \right)$$ wherekTf _∞ is the bulk free energy per unit volume, ζ(x) denotes the Riemann zeta function, andΓ(x) denotes the gamma function. With 1/W identified askT, this result is precisely the low-temperature behavior of the free energy of a (d?1)-dimensional Debye solid. This fact is explained in terms of an equivalence between the Coulomb gas and quantum fields. Also, the expansion is verified for some exactly solved models of Coulomb systems in two dimensions.     

Dynamics of a vertical flight in the stationary gravitational field of a celestial body: Post-newtonian corrections and gravitational redshift

The standard problem of a radial motion of test particles in the stationary gravitational field of a spherically symmetric celestial body is solved and is used to determine the time features of this motion. The problem is solved for the equations of motion of general relativity (GR), and the time features are obtained in the post-Newtonian approximation, with linear GR corrections proportional to r _g /r and β ² (in the solution being considered, they are of the same order of smallness) being taken rigorously into account. Total times obtained by integrating the time differentials along the trajectories of motion are considered as the time features in question. It is shown that, for any parameters of the motion, the proper time (which corresponds to watches comoving with a test particle) exceeds the time of watches at rest (watches at the surface of the celestial body being considered). The mass and the radius of the celestial body, as well as the initial velocity of the test particle, serve as arbitrary parameters of the motion. The time difference indicated above implies a leading role of the gravitational redshift, which decreases somewhat because of the opposite effect of the Doppler shift. The results are estimated quantitatively for the important (from the experimental point of view) case of vertical flights of rockets starting from the Earth’s surface. In this case, the GR corrections, albeit being extremely small (a few microseconds for several hours of the flight), aremeasurable with atomic (quantum) watches.     

Relativistic corrections to the energy levels of hydrogen atoms in a strong magnetic field

Relativistic corrections to the binding energies of various states of the strongly magnetized hydrogen atom are estimated by a perturbation calculation.     

On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordström space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.     

Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field

We use a simple method to calculate interface properties of the square-lattice Ising antiferromagnet with nearest neighbour interaction. The method bypasses the more complicated bulk problem by taking into account only interface configurations of spins and allows the inclusion of a finite magnetic field. From this we derive two new results: 1) the interface free energy associated with the coexistence of the two antiferromagnetic phases at finite magnetic field, and 2) the transition temperature as a function of the magnetic field which determines the phase boundary.     

Cosmological constant and quantum gravitational corrections to the running fine structure constant

The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.     

Radiative corrections to positronium energy levels

A systematic perturbation theory for the computation of positronium energy levels is presented. The proposed method is based on the Bethe-Salpeter equation and a zeroth-order kernel for which exact solutions are known explicitly. The cancellation of ultraviolet divergences arising in the perturbation series is discussed, and new contributions to the ground-state hyperfine splitting of positronium are evaluated up to order α⁶.     

Relativistic corrections to Coulomb energy calculations

Coulomb energies of nuclei have been calculated using a recently introduced relativistic nuclear shell model¹). The results are very close to those of the usual non-relativistic, isotropic harmonic oscillator shell model, showing the most deviation for heavy elements such as lead.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化