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M. V. Cougo-Pinto

Publications and source records attributed to M. V. Cougo-Pinto.

17 recordsLinked to original sources
arXiv2019

An Integrodifferential Equation for Electromagnetic Fields in Linear Dispersive Media

We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in Fourier space. However, it can be rewarding to consider these properties as causal functions of time. Due to temporal non locality, this procedure gives rise to an integrodifferential equation for the electromagnetic fields, which we also call a wave equation. We have not found this equation in the literature and we show in this paper why it can be useful.

physics.class-ph↗
arXiv2010

Past and future blurring at fundamental length scale

We obtain the $κ$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2κ)$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.

hep-th↗
arXiv2008

Primitively divergent diagrams in $κ$-deformed scalar field with quartic self-interaction

We obtain the primitively divergent diagrams in $κ$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2κ)$ on such diagrams. Thanks to $κ$-deformation, we find that the dimensionally regularized forms of the diagrams lead to finite results in the limit of space-time dimension four. The effect of the deformation appears as a displacement of the poles in the complex plane.

hep-th↗
arXiv2003

Kappa-deformed quantum field theory and Casimir effect

We consider the quantization of a scalar kappa-deformed field up to the point of obtaining an expression for its vacuum energy. The expression is given by the half sum of the field frequencies, as in the non-deformed case, but with the frequencies obeying the kappa-deformed dispersion relation. We consider a set of kappa-deformed Maxwell equations and show that for the purpose of calculating the Casimir energy the Maxwell field, as in the non-deformed case, behaves as a pair of scalar fields. Those results provide a foundation for computing the Casimir energy starting from the the half sum of field frequencies. A method of calculation starting from this expression is briefly described.

hep-th↗
arXiv2003

The relation between effective action and vacuum energy in a kappa-deformed theory

In a quantum field with spacetime invariance governed by the Poincare algebra the one-loop effective action is equal to the sum of zero modes frequencies, which is the vacuum energy of the field. The first Casimir invariant of the Poincare algebra provides the proper time Hamiltonian in Schwinger's proper time representation of the effective action. We consider here a massive neutral scalar field with spacetime invariance governed by the so called kappa-deformed Poincare algebra. We show here that if in the kappa-deformed theory the first Casimir invariant of the algebra is also used as the proper-time hamiltonian the effective action appears with a real and an imaginary part. The real part is equal to half the sum of kappa-deformed zero mode frequencies, which gives the vacuum energy of the kappa-deformed field. In the limit in which the deformation disappears this real part reduces to half of the sum of zero mode frequencies of the usual scalar field. The imaginary part is proportional to the sum of the squares of the kappa-deformed zero mode frequencies. This part is a creation rate of field excitations in the situations in which it gives rise to a finite physically meaningful quantity. This is the case when the field is submitted to boundary conditions and properly renormalized, as we show in a related paper.

hep-th↗
arXiv2003

The creation of kappa deformed electromagnetic radiation from a sum of zero modes

In a related paper we have obtained that the effective action for a kappa-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the kappa-deformed zero mode frequencies, while the imaginary part is proportional to the sum of the squares of the zero mode frequencies, being proportional to the inverse of kappa. Here we calculate this imaginary part for the kappa-deformed electromagnetic field confined between two perfectly conducting parallel plates. After renormalization this imaginary part gives a creation rate of kappa-deformed electromagnetic radiation. This creation rate goes to zero at the appropriate limits, namely: when the deformation disappears or at infinite separation of the plates. The result agrees with previously obtained results and shed light on them by exhibiting the creation rate as originated in a sum of zero modes. Let us note that due to the rather complicated kappa-deformed electromagnetic dispersion relation we were led to the theorem of the argument in order to sum the squares of the kappa-deformed frequencies.

hep-th↗
arXiv2001

Vacuum confinement at finite temperature for scalar QED in magnetic field and deformed boundary condition

We investigate the Casimir effect at finite temperature for a charged scalar field in the presence of an external uniform and constant magnetic field, perpendicular to the Casimir plates. We have used a boundary condition characterized by a deformation parameter $θ$; for $θ=0$ we have a periodic condition and for $θ=π$, an antiperiodic one, for intermediate values, we have a deformation. The temperature was introduced using the imaginary time formalism and both the lagrangian and free energy were obtained from Schwinger proper time method for computing the effective action. We also computed the permeability and its asymptotic expressions for low and high temperatures.

hep-th↗
arXiv1999

Magnetic permeability of constrained scalar QED vacuum

We compute the influence of boundary conditions on the Euler-Heisenberg effective Lagrangian scalar QED scalar for the case of a pure magnetic field. The boundary conditions constrain the quantum scalar field to vanish on two parallel planes separeted by a distance $a$ and the magnetic field is assumed to be constant, uniform and perpendicular to the planes. The effective Lagrangian is obtained using Schwinger's proper-time representation and exhibits new contributions generated by the boundary condition much in the same way as a material pressed between two plates exhibits new magnetic properties. The confined bosonic vacuum presents the expected diamagnetic properties and besides the new non-linear $a$-dependent contributions to the susceptibility we show that there exists also a new $a$-dependent contribution for the vacuum permeability in the linear approximation.

hep-th↗
arXiv1999

Bosonic Casimir effect in external magnetic field

We compute the influence of an external magnetic field on the Casimir energy of a massive charged scalar field confined between two parallel infinite plates. For this case the obtained result shows that the magnetic field inhibits the Casimir effect.

hep-th↗
arXiv1998

Magnetic properties of confined bosonic vacuum at finite temperature

We compute the combined effect of confinement, an external magnetic field and temperature on the vacuum of the charged scalar field using Schwinger's formula for the effective action in the imaginary time formalism. The final result reproduces an effective Lagrangian similar to the Heisenberg-Euler one in the limit of no confinement, in the case of confinement it provides the necessary corrections to this Lagrangian at each order of magnitude of the magnetic field. The results show a finite temperature contribution to the vacum permeability constant apart from the one due to confinement alone.

hep-th↗
arXiv1998

QED vacuum between an unusual pair of plates

We consider the photon field between an unusual configuration of infinite parallel plates: a perfectly conducting plate $(ε\to\infty)$ and an infinitely permeable one $μ\to\infty)$. After quantizing the vector potential in the Coulomb gauge, we obtain explicit expressions for the vacuum expectation values of field operators of the form $<{\hat E}_i{\hat E}_j>_0$ and $<{\hat B}_i{\hat B}_j>_0$. These field correlators allow us to reobtain the Casimir effect for this set up and to discuss the light velocity shift caused by the presence of plates (Scharnhorst effect \cite{Scharnhorst,Barton,BarScharn}) for both scalar and spinor QED.

hep-th↗
arXiv1998

Casimir effect at finite temperature of charged scalar field

The Casimir effect for Dirac as well as for scalar charged particles is influenced by external magnetic fields. It is also influenced by finite temperature. Here we consider the Casimir effect for a charged scalar field under the combined influence of an external magnetic field and finite temperature. The free energy for such a system is computed using Schwinger's method for the calculation of the effective action in the imaginary time formalism. We consider both the limits of strong and weak magnetic field in which we compute the Casimir free energy and pressure.

hep-th↗
arXiv1998

Fermionic Casimir effect in an external magnetic field

The influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field under antiperiodic (and periodic) boundary condition is computed by applying Schwinger's proper time method. The result thus obtained shows that in principle, under suitable conditions, the magnetic field can enhance the fermionic Casimir energy density.

hep-th↗
arXiv1998

Magnetic Permeability of Constrained Fermionic Vacuum

We obtain using Schwinger's proper time approach the Casimir-Euler-Heisenberg effective action of fermion fluctuations for the case of an applied magnetic field. We implement here the compactification of one space dimension into a circle through anti-periodic boundary condition. Aside of higher order non-linear field effects we identify a novel contribution to the vacuum permeability. These contributions are exceedingly small for normal electromagnetism due to the smallness of the electron Compton wavelength compared to the size of the compactified dimension, if we take the latter as the typical size of laboratory cavities, but their presence is thought provoking, also considering the context of strong interactions.

hep-th↗
arXiv1994

Schwinger's Method for the Massive Casimir Effect

We apply to the massive scalar field a method recently proposed by Schwinger to calculate the Casimir effect. The method is applied with two different regularization schemes: the Schwinger original one by means of Poisson formula and another one by means of analytical continuation.

hep-th↗
arXiv1993

A modified Schwinger's formula for the Casimir effect

After briefly reviewing how the (proper-time) Schwinger's formula works for computing the Casimir energy in the case of "scalar electrodynamics" where the boundary conditions are dictated by two perfectly conducting parallel plates with separation "a" in the Z-axis, we propose a slightly modification in the previous approach based on an analytical continuation method. As we will see, for the case at hand our formula does not need the use of Poisson summation to get a (renormalized) finite result.

hep-th↗