scholarly journals CASIMIR ENERGY OF MASSLESS FERMIONS IN THE SLAB-BAG

1999 ◽  
Vol 14 (34) ◽  
pp. 2353-2361 ◽  
Author(s):  
R. D. M. DE PAOLA ◽  
R. B. RODRIGUES ◽  
N. F. SVAITER

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space–time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta-function regularization procedure is used and it is found that the regularized zero-point energy density is finite for any number of space–time dimensions. We present a general expression for the Casimir energy of the fermionic field in such a situation.

1995 ◽  
Vol 10 (07) ◽  
pp. 619-625 ◽  
Author(s):  
R. JÁUREGUI ◽  
C. VILLARREAL ◽  
S. HACYAN

The quantum theory of fields with moving boundary conditions in four-dimensional space-time is studied. We consider the particular case of a scalar massless field between two infinite parallel plates moving with constant relative velocity. It is shown that this motion produces squeezed states, and creates 'particles' at the expense of the Casimir energy.


1991 ◽  
Vol 06 (16) ◽  
pp. 1453-1457 ◽  
Author(s):  
R. P. ZAIKOV

It is shown that in D = 3 space-time dimensions there exist a topological term for the bosonic strings. The corresponding constraints satisfy the same Virasoro algebra as the ordinary bosonic strings. These results are generalized for an arbitrary dimensional space-time if we have SO (1, 2) ⊗ O (D − 3) or SO (3) ⊗ O (1, D − 4) symmetry instead of SO (1, D − 1) space-time symmetry. A gauge-dependent correction to the Casimir energy corresponding to this topological term is derived.


2014 ◽  
Vol 29 (30) ◽  
pp. 1430068 ◽  
Author(s):  
Xiang-Hua Zhai ◽  
Rui-Hui Lin ◽  
Chao-Jun Feng ◽  
Xin-Zhou Li

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some unclear points. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the p-dimensional cavity in (D + 1)-dimensional space–time, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.


1999 ◽  
Vol 14 (02) ◽  
pp. 281-300 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
ALEXANDER YU. KAMENSHCHIK ◽  
KLAUS KIRSTEN

The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential Aμ, and on the ghost fields. The scheme requires that temporal and tangential components of Aμ perturbations should vanish at the boundary, jointly with the gauge-averaging functional, first chosen to be of the Lorentz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of Aμ, jointly with the decoupled normal mode of Aμ. Moreover, normal and longitudinal components of Aμ for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in noncovariant gauges.


1990 ◽  
Vol 68 (1) ◽  
pp. 1-10
Author(s):  
Ray Skinner ◽  
Ken Wong

It is shown that it is necessary to add a boundary term to the conventional action for the Dirac fermion field. This is verified for massless fermions in a two-dimensional space–time by exact calculations of the path integrals for various transition amplitudes over a finite time interval.


Author(s):  
Shinichi Ishiguri

In our previous papers [1,3], using only the concepts of the zero-point energy and quantized space–times, all the fields including gravity were explained. However, the previous papers had the following limitations: First, the concept of the quantized space-time must be experimentally confirmed. Second, we should clarify the meaning of the quantized Einstein’s gravity equation, which is derived in [1]. Moreover, in another paper [2], we succeeded in describing the neutrinos’ self-energy and their oscillations. However, this paper assumes the rest energy of 3-leptons in advance, which is why we needed to uncover the reason why leptons have 3-generations. As mentioned, using the concepts of the zero-point energy and quantized space–times, we derived the quantized Einstein’s gravity equation in our previous paper [1]. The paper provides an analytical solution of this equalized Einstein’s equation, which implies the conservation of angular momentum in terms of quantized space–times. Employing this solution and without the standard big bang model, a unique form of acceleration equation for the acceleration-expansion universe is derived. Moreover, the temperature of the cosmic microwave background (CMB) emission is also obtained. Further, this solution results in an analytical (not numerical) derivation of the gravity wave. Moreover, based on the configuration of quantized space–times in terms of both electric and magnetic fields, we analytically attempted to calculate every equation in terms of electromagnetic and gravity fields, using the solution of the quantized Einstein’s gravity equation. As a result of this theory, first the calculated acceleration and temperature of CMB emission agree with the measurements. Furthermore, the analytical solution of the quantized Einstein’s gravity equation resulted in all the laws of electromagnetic and gravity fields in addition to the analytically derived gravity wave, which agrees well with the recent measurements. Moreover, the calculations of the energies in the basic configuration of the quantized space–times resulted in all 3-leptons’ rest energies. Considering this basic configuration is uniformly distributed everywhere in the universe, we can conclude that τ-particles or static magnetic field energy derived from the basic configuration of the quantized space–times is the identity of dark energy, which also distributes uniformly in the universe.


2014 ◽  
Vol 29 (05) ◽  
pp. 1450024 ◽  
Author(s):  
E. Arias ◽  
J. G. Dueñas ◽  
N. F. Svaiter ◽  
C. H. G. Bessa ◽  
G. Menezes

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations, we introduce a space–time dependent random coefficient in the Klein–Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance a. The correction to the renormalized vacuum energy density between the plates goes as 1/a8 instead of the usual 1/a4 dependence for the free case. In turn, we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.


2019 ◽  
Author(s):  
Vitaly Kuyukov

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.


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