arXiv subjects
Publications and source records attributed to A C Tort.
The electrostatic field energy due to two fixed pointlike charges shows some peculiar features concerning the distribution in space of the field energy density of the system. Here we discuss the evaluation of the field energy and the mathematical details that lead to those peculiar and non-intuitive physical features.
We discuss the flat and hollow models of the Earth as a pedagogical example of the application of Gauss' law to the gravitational field.
We discuss an alternative non-perturbative proof of Bertrand's theorem that leads in a concise way directly to the two allowed fields: the newtonian and the isotropic harmonic oscillator central fields.
We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple elastic function can be inferred are discussed and the normal modes and normal frequencies obtained. An approximation procedure to the evaluation of the normel frequencies in the case of uniform elastic function and mass density is also discussed.
We review a simple technique for evaluating the vacuum energy stemming from non-trivial boundary conditions and review results for the Casimir energy of a massive fermionic field confined in a d+1-dimensional slab-bag and the effect of a uniform magnetic field on the vacuum energy of confined massive bosonic and fermionic fields. New results concerning the Casimir energy and the evaluation of the rate of creation of quanta in kappa-deformed theories are presented.
We discuss the work-kinetic energy theorem and the mechanical energy conservation theorem in the context of general physics courses. The motivation is the fact that all modern texts on introductory mechanics show the same conceptually dangerous statement that besides obliterating the concept of mechanical work, diminishing the importance of the work-kinetic energy theorem, leads to erroneous applications of the energy conservation theorem and at the same eliminates its relationship with the principle of the conservation of the mechanical momentum.
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as electrostatic energy, force and torque associated with this configuartion are fully discussed. Possible variants of the problem are also discussed.
We work with $N-$dimensional compact real hyperbolic space $X_Γ$ with universal covering $M$ and fundamental group $Γ$. Therefore, $M$ is the symmetric space $G/K$, where $G=SO_1(N,1)$ and $K=SO(N)$ is a maximal compact subgroup of $G$. We regard $Γ$ as a discrete subgroup of $G$ acting isometrically on $M$, and we take $X_Γ$ to be the quotient space by that action: $X_Γ=Γ\backslash M = Γ\backslash G/K$. The natural Riemannian structure on $M$ (therefore on $X$) induced by the Killing form of $G$ gives rise to a connection $p-$form Laplacian ${\frak L}_p$ on the quotient vector bundle (associated with an irreducible representation of K). We study gauge theories based on abelian $p-$forms on the real compact hyperbolic manifold $X_Γ$. The spectral zeta function related to the operator ${\frak L}_p$, considering only the co-exact part of the $p-$forms and corresponding to the physical degrees of freedom, can be represented by the inverse Mellin transform of the heat kernel. The explicit thermodynamic fuctions related to skew-symmetric tensor fields are obtained by using the zeta-function regularization and the trace tensor kernel formula (which includes the identity and hyperbolic orbital integrals). Thermodynamic quantities in the high and low temperature expansions are calculated and new entropy/energy ratios established.
We re-evaluate the zero point Casimir energy for the case of a massive scalar field in $\mathbf{R}^{1}\times\mathbf{S}^{3}$ space, allowing also for deviations from the standard conformal value $ξ=1/6$, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularisation of the vacuum energy.
We argue that the temperature inversion symmetry present in the original Casimir setup and also in other Casimir systems for which symmetrical boundary conditions are imposed is not related to the duality transformations that in the context defined in Ref. [1] are transformations relating spatial extension and temperature, and pressure and energy density. We provide an example of a Casimir system for which in principle there is no temperature inversion symmetry but nevertheless these duality transformations can be found.