اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSome Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
104
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the $p$-dimensional cavity in ($D+1$)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.
قيم البحث
اقرأ أيضاً
We reconsider the thermal scalar Casimir effect for $p$-dimensional rectangular cavity inside $D+1$-dimensional Minkowski space-time. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Ab
el-Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of $D$=3, $p$=1 and $D$=3, $p$=3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for $D>p$ and $D=p$ cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for $D>p$, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for $D=p$, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find with the side length going to infinity the force always tends to zero for different boundary conditions regardless of $D>p$ or $D=p$. The Casimir free energy and force at high temperature limit behave asymptotically alike in that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem.
We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in $d$-dimensions. The eigenvectors of a fishnet lattice of length $L$ depend on a set of $L$ quantum numbers $(u_
k,l_k)$, each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in $(1+1)$-dimensions with $O(d)$ internal symmetry, and the wave-functions are formally constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. These properties are proved via the representation - new to our knowledge - of the matrix elements of the fused R-matrix with $O(d)$ symmetry as integral operators on the functions of two spacetime points. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions.
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous studies where
the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: $boldsymbol{ abla} cdot mathbf{E}= (2lambda/alpha)delta(r)/r$. Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self--adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, S-matrix and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the S-matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.
We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field. As geometry of boundari
es we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel-Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy-momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative al large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy-momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy-momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.
Holographic tensor networks associated to tilings of (1+1)-dimensional de Sitter spacetime are introduced. Basic features of these networks are discussed, compared, and contrasted with conjectured properties of quantum gravity in de Sitter spacetime.
Notably, we highlight a correspondence between the quantum information capacity of the network and the cosmological constant.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
