In this paper we investigate the Casimir energy for systems with the lifetime of particles. We believe that all of the scales that naturally appear in the formulation of the problem in terms of a lagrangian and the set of boundary conditions, as internal scales. We defi More
In this paper we investigate the Casimir energy for systems with the lifetime of particles. We believe that all of the scales that naturally appear in the formulation of the problem in terms of a lagrangian and the set of boundary conditions, as internal scales. We define all other scales such as lifetime of particles as external scales. One of the first effects of these external scales is the restrictions could be apply on the allowed modes in the zero point energy of a system. In this paper we show how these scales (for example the finite lifetime of particles) produce restrictions on the allowed modes, which alter the Casimir energy. We compare our results with those reported in the literature, which are invariably devoid of such scales, and show that the difference increases when the internal scales of the problem approach the external scales. In order to describe above effects, we use the generic and simple example of a massive scalar field confined between two points with Dirichlet boundary conditions in one spatial dimension.
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In this paper we investigate the Casimir energy for systems with the finite size of composite particles. We believe that all of the scales that naturally appear in the formulation of the problem in terms of a lagrangian and the set of boundary conditions, as internal sc More
In this paper we investigate the Casimir energy for systems with the finite size of composite particles. We believe that all of the scales that naturally appear in the formulation of the problem in terms of a lagrangian and the set of boundary conditions, as internal scales. We define all other scales such as the finite size of composite particles as external scales. One of the first effects of these external scales is the restrictions could be apply on the allowed modes in the zero point energy of a system. In this paper we show how these scales (for example the finite size of composite particles) produce restrictions on the allowed modes, which alter the Casimir energy. We compare our results with those reported in the literature, which are invariably devoid of such scales, and show that the difference increases when the internal scales of the problem approach the external scales. In order to describe above effects, we use the generic and simple example of a massive scalar field confined between two points with Dirichlet boundary conditions in one spatial dimension.
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In this paper we investigate the Casimir energy for systems with Periodic Boundary Conditions (PBCs) on a two dimensional sphere (S^2) by Similar Configurations Subtraction Scheme (SCSS). The SCSS is a slight modification of Boyer's subtraction method to remove divergen More
In this paper we investigate the Casimir energy for systems with Periodic Boundary Conditions (PBCs) on a two dimensional sphere (S^2) by Similar Configurations Subtraction Scheme (SCSS). The SCSS is a slight modification of Boyer's subtraction method to remove divergences which led to the bare parameters in the Casimir energy calculation. In this paper we first use this method for a problem in a curved space-time. For more simplicity we purpose a system with PBCs on a sphere with radius a and its scalar curvature R=2a^(-2). Usually, in the SCSS to remove divergences from zero point energy expressions, two comparable configurations have been designed and then the zero point energies of these two configurations are subtracted from each other. This setup for configurations made us an ability to divide divergences clearly and it would be to show all divergences are removed without resorting to any other techniques such as analytic continuation techniques. In final we compare our results with those reported in the literature, which are obtained from other regularization techniques.
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In this paper we investigate the Casimir energy for systems with Anti-Periodic Boundary Conditions (BCs) in one spatial dimension by Box Subtraction Scheme (BSS). The BSS is a slight modification of Boyer's subtraction method to remove divergences from expressions in th More
In this paper we investigate the Casimir energy for systems with Anti-Periodic Boundary Conditions (BCs) in one spatial dimension by Box Subtraction Scheme (BSS). The BSS is a slight modification of Boyer's subtraction method to remove divergences from expressions in the Casimir energy calculation. The more routine method which involves many regularization and analytic continuation procedures has some ambiguities. These ambiguities have been described recently in some papers. However, in this paper we shall investigate some of them and also we describe the main ingredient of the BSS in the subtraction of two comparable configurations for our problem. Usually, two approaches in the Leading order Casimir energy are yield identical results but the latter regularization has more manifest way to remove divergences from expressions. So it could be the best instrument for us to remove complicated divergences which appear in the higher order radiative corrections to the Casimir energy. Extracting and obtaining of finite results from complicated divergent expressions without resorting to any analytic continuation techniques is also the other privilege of the BSS. In this paper we use this regularization method to obtain the Casimir energy and in final we compare our results with those reported in the literature, which are obtained from other regularization techniques.
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In this paper we investigate the Casimir energy for systems with Periodic Boundary Conditions (PBCs) on a two dimensional sphere (S^2) by Box Subtraction Scheme (BSS). The BSS is a slight modification of Boyer's subtraction method to remove divergences from expressions More
In this paper we investigate the Casimir energy for systems with Periodic Boundary Conditions (PBCs) on a two dimensional sphere (S^2) by Box Subtraction Scheme (BSS). The BSS is a slight modification of Boyer's subtraction method to remove divergences from expressions in the Casimir energy calculation. The BSS have been used in many calculations of the Casimir energy for configurations which all designed in a flat space-time. However, in this paper we first use this method for a problem in a curved space-time. For more simplicity we purpose a system with PBCs on a sphere with radius a and its scalar curvature R=2a^(-2). Usually, in the BSS to remove divergences from zero point energy expressions, two comparable configurations have been designed and then the zero point energies of these two configurations are subtracted from each other. This setup for configurations made us an ability to divide divergences clearly and it would be to show all divergences are removed without resorting to any other techniques such as analytic continuation techniques. In final we compare our results with those reported in the literature, which are obtained from other regularization techniques.
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In this article we investigate the Casimir energy for massive and massless scalar field on 3- sphere with S^3 topology by Box Subtraction Scheme (BSS). This method spontaneously eliminate divergences that is appeared in the Casimir energy calculation process. Usually, i More
In this article we investigate the Casimir energy for massive and massless scalar field on 3- sphere with S^3 topology by Box Subtraction Scheme (BSS). This method spontaneously eliminate divergences that is appeared in the Casimir energy calculation process. Usually, in the BSS to remove divergences from zero point energy expressions, two comparable configurations are designed and then the zero point energies of these two configurations are subtracted from each other. This setup for configurations made us an ability to divide divergences clearly and it would be to show all divergences are removed without resorting to any other techniques such as analytic continuation techniques. In final we compare our results with those reported in the literature, which are obtained from other regularization techniques.
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