Radiative correction to the Dirichlet Casimir energy for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>λ</mml:mi><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> theory in two spatial dimensions

Gousheh, S. S.; Moazzemi, Reza; Valuyan, M. A.

doi:10.1016/j.physletb.2009.10.058

Cited by 22 publications

(27 citation statements)

References 48 publications

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“…The renormalization procedure, the deduction of the counter-terms, and the final general form of the first order vacuum energy have been completely discussed in Refs. [20,23]. Therefore, in this paper, we use only the important conclusions.…”

Section: First Order Radiative Correctionmentioning

confidence: 99%

“…This statement necessities using the position-dependent counter-terms instead of free counter-terms in the renormalization program. This viewpoint on renormalization program has been explained in detail in previous studies [20][21][22][23][24][25][26][27] and all their physical aspects and advantages have been discussed. The same idea in the renormalization of interacting quantum field theory in the curved space time has been extensively investigated [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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

Valuyan

2017

Mod. Phys. Lett. A

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In this paper, the first order radiative correction to the Casimir energy for a massive scalar field in the φ 4 theory on a spherical surface with S 2 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 counterterms 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.

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Section: First Order Radiative Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Valuyan

2017

Mod. Phys. Lett. A

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“…The radiative correction to the Casimir energy for φ 4 theory confined between two parallel lines with Dirichlet boundary conditions in 2 + 1 dimensions was obtained as a divergent result (17; 18). This quantity, by changing the counterterms to position-dependent ones, which is consistent with the dominant boundary conditions, is to be convergent (19). The use of the position-dependent counterterms in the calculation of the radiative correction to the Casimir energy for different geometries with various quantum fields and boundary conditions was examined in (20; 21; 22).…”

Section: Introductionmentioning

confidence: 99%

“…This complexity commonly originates from the kind of divergences appearing in the vacuum energy, since the type of divergent expression appeared in the vacuum energy of systems in even spatial dimensions is usually logarithmic, and the removal process of this type of divergence is more difficult than that of the other types of divergence. The successful experience of the aforementioned renormalization program supplemented by BSS as a regularization technique in (19) motivated us to calculate the radiative correction to the Casimir energy for a massive and massless scalar field with mixed boundary conditions in 2 + 1 dimensions. The remainder of this work is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Radiative Correction to The Casimir Energy with Mixed Boundary Condition in 2+1 Dimensions

Valuyan

2020

Preprint

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In the present study, the zero-and first-order radiative correction to the Casimir energy for the massive and massless scalar field confined with mixed (Neumann-Dirichlet) boundary condition between two parallel lines in 2 + 1 dimensions for the self-interacting φ 4 theory was computed. The main point in this study is the use of a special program to renormalize the bare parameters of the Lagrangian. The counterterm used in the renormalization program, which was obtained systematically position-dependent, is consistent with the boundary condition imposed on the quantum field. To regularize and remove infinities in the calculation process of the Casimir energy, the Box Subtraction Scheme as a regularization technique was used. In this scheme, two similar configurations are usually introduced, and the vacuum energies of these two configurations in proper limits are subtracted from each other. The final answer for the problem is finite and consistent with the expected physical basis. We also compared the new result of this paper to the previously reported results in the zero-and first-order radiative correction to the Casimir energy of scalar field in two spatial dimensions with Periodic, Dirichlet, and Neumann boundary conditions. Finally, all aspects of this comparison were discussed.

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“…The Casimir energy and the resulting forces have been investigated for different fields in different geometries and boundary conditions [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In some of these investigations the Casimir forces on the boundaries are also calculated.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

2014

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We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and the strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs show considerable sensitivity to the fine details of the shape of the background field which cannot be seen from the graph of the total Casimir energy. Finally, we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.

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Radiative correction to the Dirichlet Casimir energy for λϕ4 theory in two spatial dimensions

Cited by 22 publications

References 48 publications

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

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

Radiative Correction to The Casimir Energy with Mixed Boundary Condition in 2+1 Dimensions

An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition

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