scholarly journals A NOTE ON THE CASIMIR ENERGY OF A MASSIVE SCALAR FIELD IN POSITIVE CURVATURE SPACE

2004 ◽  
Vol 19 (02) ◽  
pp. 111-116 ◽  
Author(s):  
E. ELIZALDE ◽  
A. C. TORT
Keyword(s):  
High Temperature ◽  
Scalar Field ◽  
Zeta Function ◽  
Vacuum Energy ◽  
Positive Curvature ◽  
Zero Point ◽  
Casimir Energy ◽  
Massive Scalar ◽  
Zero Temperature ◽  
Massive Scalar Field

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in R1×S3 space, allowing also for deviations from the standard conformal value ξ=1/6, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. The analytic continuation can be performed in two ways, which are seen to be equivalent.

scholarly journals Casimir energy and topological mass for a massive scalar field with Lorentz violation

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
M. B. Cruz ◽  
E. R. Bezerra de Mello ◽  
H. F. Santana Mota
Keyword(s):  
Scalar Field ◽  
Lorentz Violation ◽  
Casimir Energy ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Topological Mass

scholarly journals Radiative correction to the Casimir energy for massive scalar field on a spherical surface

2017 ◽  
Vol 32 (24) ◽  
pp. 1750128 ◽  
Author(s):  
M. A. Valuyan
Keyword(s):  
Scalar Field ◽  
Radiative Correction ◽  
Spherical Surface ◽  
Perturbation Expansion ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Free Theory

In this paper, the first-order radiative correction to the Casimir energy for a massive scalar field in the [Formula: see text] theory on a spherical surface with [Formula: see text] topology was calculated. In common methods for calculating the radiative correction to the Casimir energy, the counter-terms related to free theory are used. However, in this study, by using a systematic perturbation expansion, the obtained counter-terms in renormalization program were automatically position-dependent. We maintained that this dependency was permitted, reflecting the effects of the boundary conditions imposed or background space in the problem. Additionally, along with the renormalization program, a supplementary regularization technique that we named Box Subtraction Scheme (BSS) was performed. This scheme presents a useful method for the regularization of divergences, providing a situation that the infinities would be removed spontaneously without any ambiguity. Analysis of the necessary limits of the obtained results for the Casimir energy of the massive and massless scalar field confirmed the appropriate and reasonable consistency of the answers.

scholarly journals Riemann zeta zeros and zero-point energy

2014 ◽  
Vol 29 (09) ◽  
pp. 1450051 ◽  
Author(s):  
J. G. Dueñas ◽  
N. F. Svaiter
Keyword(s):  
Scalar Field ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Vacuum Energy ◽  
Zero Point ◽  
Point Energy ◽  
Nontrivial Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Adjoint Operators

The sequence of nontrivial zeros of the Riemann zeta function is zeta regularizable. Therefore, systems with countably infinite number of degrees of freedom described by self-adjoint operators whose spectra is given by this sequence admit a functional integral formulation. We discuss the consequences of the existence of such self-adjoint operators in field theory framework. We assume that they act on a massive scalar field coupled to a background field in a (d+1)-dimensional flat space–time where the scalar field is confined to the interval [0, a] in one of its dimensions and there are no restrictions in the other dimensions. The renormalized zero-point energy of this system is presented using techniques of dimensional and analytic regularization. In even-dimensional space–time, the series that defines the regularized vacuum energy is finite. For the odd-dimensional case, to obtain a finite vacuum energy per unit area, we are forced to introduce mass counterterms. A Riemann mass appears, which is the correction to the mass of the field generated by the nontrivial zeros of the Riemann zeta function.

scholarly journals Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach

2018 ◽  
Vol 96 (9) ◽  
pp. 1004-1009 ◽  
Author(s):  
M.A. Valuyan
Keyword(s):  
Scalar Field ◽  
Spherical Surface ◽  
Original System ◽  
Large Mass ◽  
Casimir Energy ◽  
Energy Calculation ◽  
Massive Scalar ◽  
Mass Limit ◽  
Massive Scalar Field ◽  
Spherical Surfaces

In this study, the Casimir energy for massive scalar field with periodic boundary condition was calculated on spherical surfaces with S1, S2, and S3 topologies. To obtain the Casimir energy on a spherical surface, the contribution of the vacuum energy of Minkowski space is usually subtracted from that of the original system. In the large mass limit for surface S2, however, some divergences would eventually remain in the obtained result. To remove these remaining divergences, a secondary renormalization program was manually performed. In the present work, a direct approach for calculation of the Casimir energy has been introduced. In this approach, two similar configurations were considered and then the vacuum energies of these configurations were subtracted from each other. This method provides more physical meaning than the other common methods. Additionally, in the large mass limit for surface S2, it provides a situation in which the second renormalization program is automatically conducted in the calculation procedure, and there was no longer a need to do so manually. Finally, by plotting the obtained values for the Casimir energy of the topologies and investigating their appropriate limits, the logic agreement between the results of our scheme and those of previous studies was discussed.

scholarly journals THE CASIMIR FORCE OF QUANTUM SPRING IN THE (D+1)-DIMENSIONAL SPACETIME

2011 ◽  
Vol 26 (09) ◽  
pp. 669-679 ◽  
Author(s):  
XIANG-HUA ZHAI ◽  
XIN-ZHOU LI ◽  
CHAO-JUN FENG
Keyword(s):  
Scalar Field ◽  
Casimir Force ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Dimensional Spacetime

The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper.27 Here, the Casimir effect of the quantum spring is investigated in (D+1)-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any D, which indicate a Z2 symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the ζ-function. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes.

scholarly journals Static Casimir condensate of conformal scalar field in Friedmann universe

2018 ◽  
Vol 33 (28) ◽  
pp. 1850162 ◽  
Author(s):  
Andrej B. Arbuzov ◽  
Alexander E. Pavlov
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Casimir Energy ◽  
Divergent Series ◽  
Massive Scalar ◽  
Friedmann Universe ◽  
Differential Relation ◽  
Static Approximation ◽  
Massive Scalar Field ◽  
Conformal Scalar Field

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel–Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived.

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