The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.
Casimir energy for a massless scalar field for a conical wedge and a conical cavity are calculated. The group generated by the images is employed in deriving the Green functions as well as the wave functions and the energy spectrum.
The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the pe…
In this paper we compute the Casimir energy and force for massless scalar fields endowed with hybrid boundary conditions, in the setting of the bounded generalized cone. By using spectral zeta function regularization methods, we obtain explicit expressions for the Casimir energy and force in arbitrary dimensions in terms of the zeta function defined on the piston. Our general formulas are, subsequently, specialized to the case in which the piston is modelled by a $d$-dimensional sphere. In this particular situation, explicit results are given for $d=2,3,4,5$.
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for a massive spinor fields in higher-dimensional spacetimes with an arbitrary number of toroidally compactified spatial dimensions. By using the Abel-Plana summation formula and the zeta function technique we present the vacuum expectation values in two different forms. Applications of the general formulae to cylindrical and toroidal carbon nanotubes are given. We show that the topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. T…
In this paper we utilize $ζ$-function regularization techniques in order to compute the Casimir force for massless scalar fields subject to Dirichlet and Neumann boundary conditions in the setting of the conical piston. The piston geometry is obtained by dividing the bounded generalized cone into two regions separated by its cross section positioned at $a$ with $a\in(0,b)$ with $b>0$. We obtain expressions for the Casimir force that are valid in any dimension for both Dirichlet and Neumann boundary conditions in terms of the spectral $ζ$-function of the piston. As a particular case, we specify…
The fermionic condensate is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. It is assumed that on the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The fermionic condensate is a periodic function of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the fermionic condensate is …
We investigate the combined effects of boundaries and topology on the vacuum expectation values (VEVs) of the charge and current densities for a massive 2D fermionic field confined on a conical ring threaded by a magnetic flux. Different types of boundary conditions on the ring edges are considered for fields realizing two inequivalent irreducible representations of the Clifford algebra. The related bound states and zero energy fermionic modes are discussed. The edge contributions to the VEVs of the charge and azimuthal current densities are explicitly extracted and their behavior in various a…
In this paper, we study the finite-temperature quantum fluctuation of a classical liquid induced by the topology of an effective conical spacetime, as well as by a quasi-periodic boundary condition. The conical spacetime could be either a disclination or a cosmic string. In this context, we consider a phonon field representing quantum excitations of the liquid density, which obeys an effective Klein- Gordon equation with the sound velocity replaced by the light velocity. We obtain closed analytic expressions for the thermal Hadamard function, and consequently, the renormalized mean square dens…
We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a (2+1)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the f…
In this work, we consider the Casimir effect due to massless fermionic fields in the presence of long cylinders. More precisely, we consider the interaction between a cylinder parallel to a plate, between two parallel cylinders outside each other, and between a cylinder lying parallelly inside another cylinder. We derive the explicit formulas for the Casimir interaction energies and compute the leading and the next-to-leading order terms of the small separation asymptotic expansions. As expected, the leading order terms coincide with the proximity force approximations. We compare the results o…
In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Ref. \cite{Feng,Zhai3} is something like that between a Möbius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the ($D+1$)-dimensional space-time. For both massless and massive cases, there is a $Z_2$ symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that…
We consider a quantum massless fermionic field in (1+1) dimensions in the case of moving boundaries. We work in the canonical approach in order to find a Hamiltonian describing the dynamics of the field. Thus, we study the statistics of work and particles produced from the vacuum by a linear driving of a boundary.
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.
We study the finite temperature Casimir interactions on two parallel boundaries in the anti-de Sitter spacetime AdS$_{D+1}$ induced by the vacuum fluctuations of a massive fermionic field with MIT bag boundary conditions. As in the Minkowski spacetime, the Casimir interaction always tends to attract the two boundaries to each other at any temperature and for any mass. For bosonic fields, it is well known that the high temperature leading term of the Casimir interaction is linear in temperature. However, for fermionic fields, the Casimir interaction decays exponentially at high temperature due …
We consider the Casimir interaction, mediated by massless fermions, between a spherical defect and a flat potential barrier, assuming hard (bag-type) boundary conditions at both the barrier and the surface of the sphere. The computation of the quantum interaction energy is carried out using the multiple scattering approach, adapted here to the setup in question. We find an exact integral formula for the energy, from which we extract both the large and short distance asymptotic behaviour. At large distance the fermionic contribution is found to scale as $L^{-3}$, in contrast to that of electrom…
The aim of this work is to investigate the role played by the fermion mass and that of an external field on the fermionic Casimir energy density under S^1 X R^3 topology. Both twisted and untwisted spin connections are considered and the exact calculation is performed using a somewhat different approach based on the combination of the analytic regularization method through alpha-representation and Euler-Maclaurin summation formula.
In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava-Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.
In this paper, we evaluate the Casimir energy and pressure for a massive fermionic field confined in the region between two parallel plates. In order to implement this confinement we impose the standard MIT bag boundary on the plates for the fermionic field. In this paper we consider a quantum field theory model with a CPT even, aether-like Lorentz symmetry violation. It turns out that the fermionic Casimir energy and pressure depend on the direction of the constant vector that implements the Lorentz symmetry breaking.
We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is $M^{p+1}\times T^q$ which has $q$ dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature r…
We evaluate the Casimir energy and force for a massive fermionic field in the geometry of two parallel plates on background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions. The bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The Casimir energy is decomposed into purely topological, single plate and interaction parts. With independence of the lengths of the compact dimensions and the phases in the periodicity conditions, the interaction part of the Casimi…
Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B(3),we give an explicit construction of the Casimir WB(3) algebras.We reserve the notation WB(N) for the Casimir W algebras of type W(2,4,6,...,2N,N+1/2) which contains one fermionic field. It is seen that WB(3) algebra is closed an associative for all values of the central element c.
We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect bag-like boundary conditions. These are simulated by the introduction of delta-like interactions with the walls. We show that, with a proper choice for the corresponding coupling constants, bag-model boundary condition are properly implemented. We obtain explicit expressions for the energies in 1+1 and 3+1 dimensions, for massless and massive fields.
The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary conditio…
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes depart from a sole dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the fundamental gauge group representation. Noticed in non-relativistic Quark Models and in a non-perturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other non-perturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie al…
We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum 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 boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phase…
In this article we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We present a new regularization mechanism the piston offers. In our case regularization occurs explicitly at the Casimir energy density and not at the Casimir force level, as in usual pistons. We make use of boundary broken supersymmetry …
We evaluate the fermionic Casimir effect associated with a massive fermion confined within a planar (d+1) dimensional slab-bag, on which MIT bag model boundary conditions of standard type, along a single spatial direction, are imposed. A simple and effective method for adding up the zero-point energy eigenvalues, corresponding to a quantum field under the influence of arbitrary boundary conditions, imposed on the field on flat surfaces perpendicular to a chosen spatial direction, is proposed. Using this procedure, an analytic result is obtained, from which small and large fermion mass limits, …
We investigate the edge effects on the finite temperature fermionic condensate (FC) for a massive fermionic field in a (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The field obeys the bag boundary condition on a circle concentric with the apex. The analysis is presented for both the fields realizing two irreducible representations of the Clifford algebra and for general case of the chemical potential. In both the regions outside and inside the circular boundary, the FC is decomposed into the boundary-free and boundary-induced contributions. They are period…
We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel-Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-…
We investigate the vacuum expectation value of the energy-momentum tensor associated with a massive fermionic field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. The asymptotic behavior of the vacuum densities is investigated near the sphere center and surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in global monopole geometry, the sphere-induced expectation values are exponentially suppressed.
The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are applicable to a field possessing any spin, and include the well-known spin-1/2 and spin-1 boundary conditions as special cases. Here we use these general boundary conditions to show that the allowed values of energy-momentum turn out to be the same for any massless fermionic field and the same for any massless bosonic field. As a result one expects to obtain only t…
We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a three-brane and two-dimensional conical space transverse to the latter. In addition, we assume the presence of an extra magnetic flux along the core of the conical space. The heat kernel and the Feynman Green function are presented in the form of a sum of two terms. The first one corresponds to the contribution coming from the bulk with global monopole in the abs…
Advanced Science Research Center, Japan Atomic Energy Agency (JAEA)（日本原子力机构先进科学研究中心）；Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；RIKEN Center for Computational Science（理化学研究所计算科学中心）
Fermionic Casimir effect in an axial Lorentz-violating background
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Universidade Estadual da Paraíba (UEPB), Centro de Ciências Exatas e Sociais Aplicadas (CCEA)（帕拉伊巴州立大学精确科学与社会科学中心）；Departamento de Física, Universidade Federal da Paraíba（帕拉伊巴联邦大学物理系）
In this work we consider a fermionic chain of finite length $\ell$. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the con…
In this paper we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT Bag Model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT Bag Model boundary condition.
The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the …
In this paper, we investigate one-loop radiative corrections to the Casimir energy in the presence of two perfectly conducting parallel plates for QED theory within the renormalized perturbation theory. In fact, there are three contributions for radiative corrections to the Casimir energy, up to order $α$. Only the two-loop diagram, which is of order $α$, has been computed by Bordag et. al (1985), approximately. Here, up to this order, we consider corrections due to two one-loop terms, i.e., photonic and fermionic loop corrections resulting from renormalized QED Lagrangian, more precisely. Our…
The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving leng…
We investigate the fermionic condensate and the vacuum expectation values of the energy-momentum tensor for a massive spinor field in de Sitter spacetime with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectation values. In this way the renormalization is reduced to the renormalization procedure in uncompactified de Sitter spacetime. It is shown that in the uncompactified su…
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 analyse 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 b…
Fermionic Casimir memory from an anisotropic gravitational pulse
Faculdade de Educação, Ciências e Letras de Iguatu（伊瓜图教育、科学与文学学院）；Universidade Estadual do Ceará（塞阿拉州立大学）；Departamento de Física, Universidade Federal da Paraíba（帕拉伊巴联邦大学物理系）
We find the free energy of the string by applying the known Matsubara formalism. Then through the Casimir effect we offer a temperature correction to the tachyon mass of the string. We see that for the fermionic part the temperature correction is precisely the opposite of that of bosonic part, so the quantum ground state of the superstring would remain massless, as expected.
Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces. In this lecture I present some results of the theory of the Casimir effect, primarily formulated in terms of Green's functions. There is an intimate relation between the Casimir effect and van der Waals forces. Applications to conductors and dielectric bodies of various shapes will be given for the cases of scalar, electromagnetic, and fermionic fields. The dimensional dependence of the effect will be described. Finally, we ask the question: Is there a connection betw…
In this paper we discuss the computation of Casimir energy on a quantum computer. The Casimir energy is an ideal quantity to calculate on a quantum computer as near term hybrid classical quantum algorithms exist to calculate the ground state energy and the Casimir energy gives physical implications for this quantity in a variety of settings. Depending on boundary conditions and whether the field is bosonic or fermionic we illustrate how the Casimir energy calculation can be set up on a quantum computer and calculated using the Variational Quantum Eigensolver algorithm with IBM QISKit. We compa…
In this paper we investigate the vacuum polarization effects associated with a massive fermionic field due to the non-trivial topology of the global monopole spacetime and boundary conditions imposed on this field. Specifically we investigate the vacuum expectation values of the energy-momentum tensor and fermionic condensate admitting that the field obeys the MIT bag boundary condition on two concentric spherical shells. In order to develop this analysis, we use the generalized Abel-Plana summation, which allows to extract from the vacuum expectation values the contribution coming from a sing…
Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces. In these lectures I present the theory of the Casimir effect, primarily formulated in terms of Green's functions. There is an intimate relation between the Casimir effect and van der Waals forces. Applications to conductors and dielectric bodies of various shapes will be given for the cases of scalar, electromagnetic, and fermionic fields. The dimensional dependence of the effect will be described. Finally, we ask the question: Is there a connection between the Casimi…
Casimir operators for the relativistic quantum phase space symmetry group
Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar)（马达加斯加国家核科学与技术研究所）；TWAS Madagascar Chapter, Malagasy Academy（非洲科学院马达加斯加分会，马达加斯加科学院）；Faculty of Sciences, iHEPMAD-University of Antananarivo（安塔那那利佛大学理学院）
