THE CASIMIR ENERGY OF A MASSIVE FERMIONIC FIELD CONFINED IN A  (d + 1)-DIMENSIONAL SLAB-BAG

Elizalde, E.; Santos, F. C.; Tort, A. C.

doi:10.1142/s0217751x03014186

Cited by 38 publications

(38 citation statements)

References 3 publications

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“…The Casimir energy with MIT boundary condition for a massive fermionic field was first computed by Mamaev and Trunov [22] (see also Ref. [3]), but can be cast into the form [23]: …”

Section: The Influence Of the Mass In The Casimir Effect: Graphical Rmentioning

confidence: 99%

Casimir effect for a massive scalar field under mixed boundary conditions

et al. 2003

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We discuss the Casimir effect for a massive bosonic field with mixed (Dirichlet-Neumann) boundary conditions. We use the ζ-function regularization prescription to obtain our physical results. Particularly, we analyse how the Casimir energy varies with the mass of the field and compare this mass dependence with those obtained for other boundary conditions. This is done graphically. Some other graphs involving a massive fermionic field are also included.

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“…The Casimir energy with MIT boundary condition for a massive fermionic field was first computed by Mamaev and Trunov [22] (see also Ref. [3]), but can be cast into the form [23]: …”

Section: The Influence Of the Mass In The Casimir Effect: Graphical Rmentioning

confidence: 99%

Casimir effect for a massive scalar field under mixed boundary conditions

et al. 2003

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“…The gluon field contribution for the Casimir effect is, up to the color quantum numbers, the same as for the electromagnetic field. For the quark field, the problem has been often addressed by considering the case of two parallel plates [49,50,51,52,53,54].…”

Section: Introductionmentioning

confidence: 99%

Thermofield dynamics and Casimir effect for fermions

et al. 2005

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A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.C. Khanna and A.E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons.

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“…Alternative expressions are derived using the expansion (e y + 1) −1 = − ∞ n=1 (−1) n e −ny . After integration one finds (no summation over µ) 22) with the notations…”

Section: Vacuum Expectation Value Of the Energy-momentum Tensormentioning

confidence: 99%

“…For arbitrary number of dimensions, the corresponding results are generalized in Refs. [21,22] for the massless and massive cases, respectively. The fermionic condensate for a massless field has been considered in Refs.…”

Section: Introductionmentioning

confidence: 99%

Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes

2011

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We investigate the fermionic condensate and the vacuum expectation value of the energymomentum tensor for a massive fermionic field in the geometry of two parallel plate on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The nontrivial topology of the background spacetime leads to an Aharonov-Bohm effect for the vacuum expectation values induced by the gauge field. The fermionic condensate and the expectation value of the energy-momentum tensor are periodic functions of the magnetic flux with period equal to the flux quantum. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phases in the periodicity conditions and of the value of the gauge potential. Interaction forces between the plates are thus always attractive.However, in physical situations where the quantum field is confined to the region between the plates, the pure topological part contributes as well, and then the resulting force can be either attractive or repulsive, depending on the specific phases encoded in the periodicity conditions along the compact dimensions, and on the gauge potential, too. Applications of the general formulas to cylindrical carbon nanotubes are considered, within the framework of a Dirac-like theory for the electronic states in graphene. In the absence of a magnetic flux, the energy density for semiconducting nanotubes is always negative. For metallic nanotubes the energy density is positive for long tubes and negative for short ones. The resulting Casimir forces acting on the edges of the nanotube are attractive for short tubes with independence of the tube chirality. The sign of the force for long nanotubes can be controlled by tuning the magnetic flux. This opens the way to the design of efficient actuators driven by the Casimir force at the nanoscale.

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THE CASIMIR ENERGY OF A MASSIVE FERMIONIC FIELD CONFINED IN A (d + 1)-DIMENSIONAL SLAB-BAG

Cited by 38 publications

References 3 publications

Casimir effect for a massive scalar field under mixed boundary conditions

Casimir effect for a massive scalar field under mixed boundary conditions

Thermofield dynamics and Casimir effect for fermions

Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes

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