arXiv subjects

V. V. Nesterenko

Publications and source records attributed to V. V. Nesterenko.

48 records · Page 3Linked to original sources

arXiv1998

Direct mode summation for the Casimir energy of a solid ball

The Casimir energy of a solid ball placed in an infinite medium is calculated by a direct frequency summation using the contour integration. It is assumed that the permittivity and permeability of the ball and medium satisfy the condition $ε_1 μ_1=ε_2μ_2$. Upon deriving the general expression for the Casimir energy, a dilute compact ball is considered $(ε_1 -ε_2)^2/(ε_1+ε_2)^2\ll 1$. In this case the calculations are carried out which are of the first order in $ξ^2$ and take account of the five terms in the Debye expansion of the Bessel functions involved. The implication of the obtained results to the attempts of explaining the sonoluminescence via the Casimir effect is shortly discussed.

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arXiv1998

Is the Casimir effect relevant to sonoluminescence?

The Casimir energy of a solid ball (or cavity in an infinite medium) is calculated by a direct frequency summation using the contour integration. The dispersion is taken into account, and the divergences are removed by making use of the zeta function technique. The Casimir energy of a dielectric ball (or cavity) turns out to be positive, it being increased when the radius of the ball decreases. The latter eliminates completely the possibility of explaining, via the Casimir effect, the sonoluminescence for bubbles in a liquid. Besides, the Casimir energy of the air bubbles in water proves to be immensely smaller than the amount of the energy emitted in a sonoluminescent flash. The dispersive effect is shown to be inessential for the final result.

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arXiv1997

Simple method for calculating the Casimir energy for sphere

A simple method for calculating the Casimir energy for a sphere is developed which is based on a direct mode summation and counter integration in a complex plane of eigenfrequencies. The method uses only classical equations determining the eigenfrequencies of the quantum field under consideration. Efficiency of this approach is demonstrated by calculation of the Casimir energy for a perfectly conducting spherical shell and for a massless scalar field obeying the Dirichlet and Neumann boundary conditions on sphere. The possibility of rationalizing the removal of divergences in this problem as a renormalization of both the energy and the radius of the sphere is discussed.

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arXiv1996

Nambu-Goto string with massive ends at finite temperature

It is shown that the critical (or deconfinement) temperature for the Nambu-Goto string connecting the point-like masses (quarks) does not depend on the value of these masses. This temperature turns out to be the same as that in the case of string with fixed ends (infinitely heavy immobile quarks).

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arXiv1995

On instability of hadronic string with heavy quarks at its ends

The quark mass dependence of the energy spectrum in the Nambu--Goto string with point--like masses (quarks) at its ends is analyzed. To this end, linearized equations of motion and boundary conditions in this model are considered. It is shown that for sufficiently large quark masses, the first excited state in string spectrum may be arbitrary close to the ground state. Obviously this points to infrared instability in the system under consideration. Possible modifications of string model which could remove this drawback are discussed.

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arXiv1995

Quark mass correction to the string potential

A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies of the Nambu--Goto string with massive ends a suitable mode--by--mode subtraction is proposed. This renormalization procedure proves to be completely unique. In the framework of the developed approach the one--loop interquark potential in the model of the relativistic string with rigidity is also calculated.

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arXiv1995

Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature

The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that for arbitrary Lagrangian function ${\cal L}(k_1)$ the general solution of the motion equations can be obtained by integrals. By analogy with the flat space--time case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in $(k_1)$ and the model of relativistic particle with maximal proper acceleration, in a space--time with constant curvature.

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arXiv1994

Dynamics of relativistic particle with Lagrangian dependent on acceleration

Models of relativistic particle with Lagrangian ${\cal L}(k_1)$, depending on the curvature of the worldline $k_1$, are considered. By making use of the Frenet basis, the equations of motion are reformulated in terms of the principal curvatures of the worldline. It is shown that for arbitrary Lagrangian function ${\cal L}(k_1)$ these equations are completely integrable, i.e., the principal curvatures are defined by integrals. The constants of integration are the particle mass and its spin. The developed method is applied to the study of a model of relativistic particle with maximal proper acceleration, whose Lagrangian is uniquely determined by a modified form of the invariant relativistic interval. This model gives us an example of a consistent relativistic dynamics obeying the principle of a superiorly limited value of the acceleration, advanced recently.

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arXiv1993

On squaring the primary constraints in a generalized Hamiltonian dynamics

Consideration of the model of the relativistic particle with curvature and torsion in the three-dimensional space-time shows that the squaring of the primary constraints entails a wrong result. The complete set of the Hamiltonian constraints arising here correspond to another model with an action similar but not identical with the initial action.

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arXiv1993

On the model of the relativistic particle with curvature and torsion

Two integrals along the world trajectory of its curvature and torsion are added to the standard action for the point-like spinless relativistic particle. Since here the three-dimensional space-time is considered at the beginning, the torsion of the world curve is defined with a sign in contrast to the previous consideration: V. V. Nesterenko, J. Math. Phys. 32, 3315 (1991). Upon obtaining a complete set of constraints in the phase space a generalized Hamiltonian description of a new version of the model is constructed. This enables one to quantize the model canonically and to derive exactly the relation between the spin and mass of the states.

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arXiv1993

Is it possible to assign physical meaning to field theory with higher derivatives?

To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in mechanical engineering. It enables one to introduce the notion of a "mechanical" energy in such field models that is wittingly positive definite. This approach can be applied at least to the higher derivative models which effectively describe the extended localized solutions in usual first order field theories (vortex solutions in Higgs models and so on). Any problems with a negative norm ghost states and unitarity violation do not arise here.

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arXiv1993

Classical dynamics of rigid string from Willmore functional

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into the space of a constant curvature. It is shown that the rigid string in flat space-time is described by the Euler-Lagrange equation for the Willmore functional in a space-time of the constant curvature K=-g/(2 a), where g and a are constants in front of the Nambu-Goto term and the curvature term in the rigid string action respectively. For simplicity the Euclidean version of the rigid string in the three-dimensional space-time is considered. The Willmore functional (the action for the "Willmore string") is obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for the rigid string. Such "reduction" of the rigid string model would be useful, for example, by applying some results about the Numbu-Goto string dynamics in the de Sitter universe to the rigid string model in the Minkowski space-time. It allows also to use numerous mathematical results about the Willmore surfaces in the context of the physical problem.

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