scholarly journals Vacuum polarization and Casimir energy of a Dirac field induced by a scalar potential in one spatial dimension

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
S. S. Gousheh ◽  
S. S. Mousavi ◽  
L. Shahkarami
Keyword(s):  
Vacuum Polarization ◽  
Scalar Potential ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
Dirac Field

scholarly journals CASIMIR ENERGY FOR A MASSIVE DIRAC FIELD IN ONE SPATIAL DIMENSION: A DIRECT APPROACH

2012 ◽  
Vol 27 (07) ◽  
pp. 1250038 ◽  
Author(s):  
R. SAGHIAN ◽  
M. A. VALUYAN ◽  
A. SEYEDZAHEDI ◽  
S. S. GOUSHEH
Keyword(s):  
Boundary Condition ◽  
Analytic Continuation ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
Dirac Field ◽  
Rigorous Derivation ◽  
Fermionic Field ◽  
Bag Model ◽  
Mit Bag Model ◽  
Massive Dirac Field

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.

CASIMIR ENERGY, FERMION FRACTIONALIZATION AND STABILITY OF A FERMI FIELD IN AN ELECTRIC POTENTIAL IN (1+1) DIMENSIONS

2012 ◽  
Vol 27 (18) ◽  
pp. 1250093 ◽  
Author(s):  
Z. DEHGHAN ◽  
S. S. GOUSHEH
Keyword(s):  
Total Energy ◽  
Electric Potential ◽  
Bound States ◽  
Vacuum Polarization ◽  
Direct Calculation ◽  
Phase Shifts ◽  
Casimir Energy ◽  
Dirac Field ◽  
Local Maxima ◽  
Densities Of States

In this paper we compute and study the Casimir energy, vacuum polarization and the resulting fermion fractionalization, the phase shifts and the stability of the bound states of a Dirac field, all due to its interaction with an electric potential in (1+1) dimension. We also explore the inter-relation between these effects. All of these effects are different manifestations of one single source, which is the distortion of the fermionic spectrum and appears as spectral deficiencies in the continua and bound states. We compute and display the spatial densities of these deficiencies and those of the bound states, along with their associated energy densities. We find that in both cases the total spatial densities of states with E > 0 and E < 0 are exact mirror images of each other. Therefore these densities for the complete spectrum are unchanged as compared to the free case, and in particular they remain uniform. The densities of states with E < 0 are precisely the vacuum polarization density and the Casimir energy density, respectively. We find that the vacuum polarization is in general noninteger. We then compute and display the energy densities of the spectral deficiencies in the momentum space, and show that levels exiting or entering the continua leave their distinctive marks on these energy densities. We also use the phase shifts to calculate the Casimir energy and obtain the same result as in the direct calculation. In this problem the Casimir energy is always positive and is on the average an increasing function of the depth and width of the potential. It has a cusp whenever an energy level crosses E = 0. These cusps are local maxima in the extreme relativistic limits. Finally we show that the taking the Casimir energy into account, the total energy will be stable under small fluctuations in the parameters of the potential. However only the first two bound states are absolutely stable in the sense that their total energy is smaller than the mass.

scholarly journals CASIMIR ENERGY AND FORCE INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

2013 ◽  
Vol 28 (31) ◽  
pp. 1350161 ◽  
Author(s):  
VOLODYMYR M. GORKAVENKO ◽  
YURII A. SITENKO ◽  
OLEXANDER B. STEPANOV
Keyword(s):  
Magnetic Flux ◽  
Vacuum Polarization ◽  
Dirichlet Boundary ◽  
Topological Defect ◽  
Casimir Energy ◽  
Matter Field ◽  
Tube Radius ◽  
Finite Radius ◽  
Polarization Effects ◽  
Scalar Matter

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

scholarly journals Scattering and Bound States of Duffin-Kemmer-Petiau Particles forq-Parameter Hyperbolic Pöschl-Teller Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hilmi Yanar ◽  
Ali Havare ◽  
Kenan Sogut
Keyword(s):  
Bound States ◽  
Scalar Potential ◽  
Spatial Dimension ◽  
Shape Parameters ◽  
Energy Eigenvalues ◽  
Vector Potentials ◽  
Scattering States ◽  
Potential Shape ◽  
Probability Densities ◽  
Interaction Approach

The Duffin-Kemmer-Petiau (DKP) equation in the presence of a scalar potential is solved in one spatial dimension for the vectorq-parameter Hyperbolic Pöschl-Teller (qHPT) potential. In obtaining complete solutions we used the weak interaction approach and took the scalar and vector potentials in a correlated form. By looking at the asymptotic behaviors of the solutions, we identify the bound and scattering states. We calculate transmission (T) and reflection (R) probability densities and analyze their dependence on the potential shape parameters. Also we investigate the dependence of energy eigenvalues of the bound states on the potential shape parameters.

scholarly journals Temporal Klein Model for Particle-Pair Creation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1361
Author(s):  
José Tito Mendonça
Keyword(s):  
Symmetry Breaking ◽  
Electric Fields ◽  
Scalar Potential ◽  
Static Field ◽  
Pair Creation ◽  
Dirac Field ◽  
Opposite Case ◽  
Time Symmetry ◽  
Electron Positron ◽  
Klein Model

This work considers the creation of electron-positron pairs from intense electric fields in vacuum, for arbitrary temporal field variations. These processes can be useful to study quantum vacuum effects with ultra-intense lasers. We use the quantized Dirac field to explore the temporal Klein model. This model is based on a vector potential discontinuity in time, in contrast with the traditional model based on a scalar potential discontinuity in space. We also extend the model by introducing a finite time-scale for potential variations. This allows us to study the transition from a singular electric field spike, with infinitesimal duration, to the opposite case of a static field where the Schwinger formula would apply. The present results are intrinsically non-perturbative. Explicit expressions for pair-creation as a function of the potential time-scales are derived. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox model, in contrast with the time symmetry breaking of the temporal Klein model.

scholarly journals Casimir Energy in a Bounded Gross-Neveu model

2018 ◽  
Vol 64 (6) ◽  
pp. 577
Author(s):  
Juan Cristóbal Rojas
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Casimir Effect ◽  
Beta Function ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
The Other ◽  
Effective Theory ◽  
Different Boundary Conditions ◽  
Complex Picture

In this letter, we study some relevant parameters of the massless Gross-Neveu (GN) model in afinite spatial dimension for different boundary conditions. It is considered the standard homogeneousHartree-Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameters used in the study.

scholarly journals DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

1999 ◽  
Vol 14 (30) ◽  
pp. 4749-4761 ◽  
Author(s):  
C. G. BENEVENTANO ◽  
M. DE FRANCIA ◽  
E. M. SANTANGELO
Keyword(s):  
Magnetic Flux ◽  
Boundary Conditions ◽  
Index Theorem ◽  
Casimir Energy ◽  
The Self ◽  
Dirac Field ◽  
Finite Region ◽  
Finite Radius ◽  
Dirac Fields ◽  
Aharonov Bohm

We study the problem of a Dirac field in the background of an Aharonov–Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behavior of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

scholarly journals Field Fluctuations and Casimir Energy of 1D-Fermions

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 643
Author(s):  
Manuel Donaire ◽  
José María Muñoz-Castañeda ◽  
Luis Miguel Nieto ◽  
Marcos Tello-Fraile
Keyword(s):  
Vacuum Energy ◽  
Normal Modes ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Dirac Field ◽  
Edge States ◽  
Vacuum Fluctuations ◽  
One Dimensional ◽  
Mass Gap ◽  
Field Fluctuations

We investigate the self-adjoint extensions of the Dirac operator of a massive one-dimensional field of mass m confined in a finite filament of length L. We compute the spectrum of vacuum fluctuations of the Dirac field under the most general dispersionless boundary conditions. We identify its edge states in the mass gap within a set of values of the boundary parameters, and compute the Casimir energy of the discrete normal modes. Two limit cases are considered, namely, that of light fermions with m L ≪ 1 , and that of heavy fermions for which m L ≫ 1 . It is found that both positive and negative energies are obtained for different sets of values of the boundary parameters. As a consequence of our calculation we demonstrate that the sign of the quantum vacuum energy is not fixed for exchange-symmetric plates (parity-invariant configurations), unlike for electromagnetic and scalar fields.

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