74 research outputs found

### Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic
field confined between two parallel plates, with MIT bag boundary conditions on
the plates. The background spacetime is $M^{p+1}\times T^q$ which has $q$
dimensions compactified to a torus. On the compact dimensions, the field is
assumed to satisfy periodicity boundary conditions with arbitrary phases. Both
the high temperature and the low temperature expansions of the Casimir free
energy and the force are derived explicitly. It is found that the Casimir force
acting on the plates is always attractive at any temperature regardless of the
boundary conditions assumed on the compact torus. The asymptotic limits of the
Casimir force in the small plate separation limit are also obtained.Comment: 10 pages, accepted by Phys. Lett.

### The Casimir effect for parallel plates at finite temperature in the presence of one fractal extra compactified dimension

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 dimension. We obtain the Casimir
energy density with the help of the regularization of multiple zeta function
with one arbitrary exponent and further the renormalized Casimir energy density
involving the thermal corrections. It is found that when the temperature is
sufficiently high, the sign of the Casimir energy remains negative no matter
how great the scale dimension $\delta$ is within its allowed region. We derive
and calculate the Casimir force between the parallel plates affected by the
fractal additional compactified dimension and surrounding temperature. The
stronger thermal influence leads the force to be stronger. The nature of the
Casimir force keeps attractive.Comment: 14 pages, 2 figure

### Conformal Mappings and Dispersionless Toda hierarchy

Let $\mathfrak{D}$ be the space consists of pairs $(f,g)$, where $f$ is a
univalent function on the unit disc with $f(0)=0$, $g$ is a univalent function
on the exterior of the unit disc with $g(\infty)=\infty$ and
$f'(0)g'(\infty)=1$. In this article, we define the time variables $t_n, n\in
\Z$, on $\mathfrak{D}$ which are holomorphic with respect to the natural
complex structure on $\mathfrak{D}$ and can serve as local complex coordinates
for $\mathfrak{D}$. We show that the evolutions of the pair $(f,g)$ with
respect to these time coordinates are governed by the dispersionless Toda
hierarchy flows. An explicit tau function is constructed for the dispersionless
Toda hierarchy. By restricting $\mathfrak{D}$ to the subspace $\Sigma$ consists
of pairs where $f(w)=1/\bar{g(1/\bar{w})}$, we obtain the integrable hierarchy
of conformal mappings considered by Wiegmann and Zabrodin \cite{WZ}. Since
every $C^1$ homeomorphism $\gamma$ of the unit circle corresponds uniquely to
an element $(f,g)$ of $\mathfrak{D}$ under the conformal welding
$\gamma=g^{-1}\circ f$, the space $\text{Homeo}_{C}(S^1)$ can be naturally
identified as a subspace of $\mathfrak{D}$ characterized by $f(S^1)=g(S^1)$. We
show that we can naturally define complexified vector fields \pa_n, n\in \Z
on $\text{Homeo}_{C}(S^1)$ so that the evolutions of $(f,g)$ on
$\text{Homeo}_{C}(S^1)$ with respect to \pa_n satisfy the dispersionless Toda
hierarchy. Finally, we show that there is a similar integrable structure for
the Riemann mappings $(f^{-1}, g^{-1})$. Moreover, in the latter case, the time
variables are Fourier coefficients of $\gamma$ and $1/\gamma^{-1}$.Comment: 23 pages. This is to replace the previous preprint arXiv:0808.072

### Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models

In this article, we derive the finite temperature Casimir force acting on a
pair of parallel plates due to a massless scalar field propagating in the bulk
of a higher dimensional brane model. In contrast to previous works which used
approximations for the effective masses in deriving the Casimir force, the
formulas of the Casimir force we derive are exact formulas. Our results
disprove the speculations that existence of the warped extra dimension can
change the sign of the Casimir force, be it at zero or any finite temperature.Comment: 9 pages, 3 figure. Final version accepted by Phys. Lett.

### Three dimensional Casimir piston for massive scalar fields

We consider Casimir force acting on a three dimensional rectangular piston
due to a massive scalar field subject to periodic, Dirichlet and Neumann
boundary conditions. Exponential cut-off method is used to derive the Casimir
energy in the interior region and the exterior region separated by the piston.
It is shown that the divergent term of the Casimir force acting on the piston
due to the interior region cancels with that due to the exterior region, thus
render a finite well-defined Casimir force acting on the piston. Explicit
expressions for the total Casimir force acting on the piston is derived, which
show that the Casimir force is always attractive for all the different boundary
conditions considered. As a function of a -- the distance from the piston to
the opposite wall, it is found that the magnitude of the Casimir force behaves
like $1/a^4$ when $a\to 0^+$ and decays exponentially when $a\to \infty$.
Moreover, the magnitude of the Casimir force is always a decreasing function of
a. On the other hand, passing from massless to massive, we find that the effect
of the mass is insignificant when a is small, but the magnitude of the force is
decreased for large a in the massive case.Comment: 22 pages, 8 figure

### Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions

We compute the finite temperature Casimir energy for massive scalar field
with general curvature coupling subject to Dirichlet or Neumann boundary
conditions on the walls of a closed cylinder with arbitrary cross section,
located in a background spacetime of the form $M^{d_1+1}\times \mathcal{N}^n$,
where $M^{d_1+1}$ is the $(d_1+1)$-dimensional Minkowski spacetime and
$\mathcal{N}^n$ is an $n$-dimensional internal manifold. The Casimir energy is
regularized using the criteria that it should vanish in the infinite mass
limit. The Casimir force acting on a piston moving freely inside the closed
cylinder is derived and it is shown that it is independent of the
regularization procedure. By letting one of the chambers of the cylinder
divided by the piston to be infinitely long, we obtain the Casimir force acting
on two parallel plates embedded in the cylinder. It is shown that if both the
plates assume Dirichlet or Neumann boundary conditions, the strength of the
Casimir force is reduced by the increase in mass. Under certain conditions, the
passage from massless to massive will change the nature of the force from long
range to short range. Other properties of the Casimir force such as its sign,
its behavior at low and high temperature, and its behavior at small and large
plate separations, are found to be similar to the massless case. Explicit exact
formulas and asymptotic behaviors of the Casimir force at different limits are
derived. The Casimir force when one plate assumes Dirichlet boundary condition
and one plate assumes Neumann boundary condition is also derived and shown to
be repulsive.Comment: 28 pages, 4 figure

### Conformal Mappings and Dispersionless Toda hierarchy II: General String Equations

In this article, we classify the solutions of the dispersionless Toda
hierarchy into degenerate and non-degenerate cases. We show that every
non-degenerate solution is determined by a function $\mathcal{H}(z_1,z_2)$ of
two variables. We interpret these non-degenerate solutions as defining
evolutions on the space $\mathfrak{D}$ of pairs of conformal mappings $(g,f)$,
where $g$ is a univalent function on the exterior of the unit disc, $f$ is a
univalent function on the unit disc, normalized such that $g(\infty)=\infty$,
$f(0)=0$ and $f'(0)g'(\infty)=1$. For each solution, we show how to define the
natural time variables $t_n, n\in\Z$, as complex coordinates on the space
$\mathfrak{D}$. We also find explicit formulas for the tau function of the
dispersionless Toda hierarchy in terms of $\mathcal{H}(z_1, z_2)$. Imposing
some conditions on the function $\mathcal{H}(z_1, z_2)$, we show that the
dispersionless Toda flows can be naturally restricted to the subspace $\Sigma$
of $\mathfrak{D}$ defined by $f(w)=1/\overline{g(1/\bar{w})}$. This recovers
the result of Zabrodin.Comment: 25 page

### Effective Electromagnetic Lagrangian at Finite Temperature and Density in the Electroweak Model

Using the exact propagators in a constant magnetic field, the effective
electromagnetic Lagrangian at finite temperature and density is calculated to
all orders in the field strength B within the framework of the complete
electroweak model, in the weak coupling limit. The partition function and free
energy are obtained explicitly and the finite temperature effective coupling is
derived in closed form. Some implications of this result, potentially
interesting to astrophysics and cosmology, are discussed.Comment: 14 pages, Revtex

### Repulsive Casimir Force from Fractional Neumann Boundary Conditions

This paper studies the finite temperature Casimir force acting on a
rectangular piston associated with a massless fractional Klein-Gordon field at
finite temperature. Dirichlet boundary conditions are imposed on the walls of a
$d$-dimensional rectangular cavity, and a fractional Neumann condition is
imposed on the piston that moves freely inside the cavity. The fractional
Neumann condition gives an interpolation between the Dirichlet and Neumann
conditions, where the Casimir force is known to be always attractive and always
repulsive respectively. For the fractional Neumann boundary condition, the
attractive or repulsive nature of the Casimir force is governed by the
fractional order which takes values from zero (Dirichlet) to one (Neumann).
When the fractional order is larger than 1/2, the Casimir force is always
repulsive. For some fractional orders that are less than but close to 1/2, it
is shown that the Casimir force can be either attractive or repulsive depending
on the aspect ratio of the cavity and the temperature.Comment: 9 pages, 3 figure

### The Casimir effect for parallel plates in the spacetime with a fractal extra compactified dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary
conditions on the parallel plates in the presence of one fractal extra
compactified dimension is analyzed. We obtain the Casimir energy density by
means of the regularization of multiple zeta function with one arbitrary
exponent. We find a limit on the scale dimension like $\delta>1/2$ to keep the
negative sign of the renormalized Casimir energy which is the difference
between the regularized energy for two parallel plates and the one with no
plates. We derive and calculate the Casimir force relating to the influence
from the fractal additional compactified dimension between the parallel plates.
The larger scale dimension leads to the greater revision on the original
Casimir force. The two kinds of curves of Casimir force in the case of
integer-numbered extra compactified dimension or fractal one are not
superposition, which means that the Casimir force show whether the
dimensionality of additional compactified space is integer or fraction.Comment: 9 pages, 3 figure

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