# 3D scalar model as a 4D perfect conductor limit: Dimensional reduction and variational boundary conditions

@article{Edery20093DSM, title={3D scalar model as a 4D perfect conductor limit: Dimensional reduction and variational boundary conditions}, author={Ariel Edery and Noah Graham and Ilana MacDonald}, journal={Physical Review D}, year={2009}, volume={79}, pages={125018} }

Under dimensional reduction, a system in D spacetime dimensions will not necessarily yield its D ― I-dimensional analog version. Among other things, this result will depend on the boundary conditions and the dimension D of the system. We investigate this question for scalar and Abelian gauge fields under boundary conditions that obey the symmetries of the action. We apply our findings to the Casimir piston, an ideal system for detecting boundary effects. Our investigation is not limited to…

## 6 Citations

### Electromagnetic Casimir piston in higher dimensional spacetimes

- Physics
- 2011

We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form MxN, where M is the four-dimensional Minkowski spacetime and N is an n-dimensional compact…

### Compatibility of the dimensional reduction and variation procedures for a quadratic curvature model with a Kaluza–Klein Ansatz

- MathematicsGeneral Relativity and Gravitation
- 2022

The introduction of extra dimensions is an invaluable strategy for the unification of gravity with other physical fields. Nevertheless, the matter in hand is to be eventually reduced to the actual 4D…

### Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

- Physics
- 2012

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified…

### Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space-time

- Physics
- 2014

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…

### Casimir pistons with curved boundaries

- Physics
- 2009

In this paper we study the Casimir force for a piston configuration in R3 with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the…

### Casimir effect for parallel plates involving massless Majorana fermions at finite temperature

- Physics
- 2010

We study the Casimir effect for parallel plates with massless Majorana fermions obeying the bag boundary conditions at finite temperature. The thermal influence will modify the effect. It is found…

## References

SHOWING 1-10 OF 40 REFERENCES

### Perfect magnetic conductor Casimir piston in d + 1 dimensions

- Physics
- 2008

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary…

### Compact dimensions and the Casimir effect: the Proca connection

- Physics
- 2008

We study the Casimir effect in the presence of an extra dimension compactified on a circle of radius R (M4 × S1 spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell…

### Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston

- Physics
- 2007

Using a multidimensional cut-off technique, we obtain expressions for the cut-off dependent part of the vacuum energy for parallelepiped geometries in any spatial dimension d. The cut-off part yields…

### Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

- Mathematics
- 2009

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on…

### Finite temperature Casimir effect in spacetime with extra compactified dimensions

- Physics, Mathematics
- 2009

### Finite-temperature Casimir effect in piston geometry and its classical limit

- Physics
- 2008

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with…

### Kaluza-Klein models as pistons

- Physics
- 2009

We consider the influence of extra dimensions on the force in Casimir pistons. Suitable analytical expressions are provided for the Casimir force in the range where the plate distance is small, and…