Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization (IR) technique in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalization constants required by the Slavnov–Taylor identities at the one-loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.     

Casimir Energy in Contact-Interaction Models

The problem of Casimir interaction between two δ ^d -like (d = 1, 2, and 3) sources in Minkowski space is examined on the basis of the ln det formalism. The result obtained for the case of two semitransparent plates (d = 1) coincides with the earlier result based on an alternative approach. The earlier assertion that there is no vacuum interaction between linear (d = 2) sources is disproved. An expression for the Casimir energy for two pointlike (d = 3) sources is obtained.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Casimir Vacuum Energy and the Semiclassical Electron

In 1953 Casimir proposed a semiclassical model for the electron based on the concept that net inward radiation pressure from the electromagnetic vacuum fluctuation fields (as in the Casimir effect, generally) might play the role of Poincare stresses, compensating outward coulomb pressure to yield a stable configuration at small dimensions. Given that in scattering experiments the electron appears point-like, critical to the success of the proposed model is demonstration that the self-energy corresponding to the divergent coulomb field does not contribute to the electron mass. Here we develop a self-consistent, vacuum-fluctuation-based model that satisfies this requirement and thereby resolves the issue of what would otherwise appear to be an incompatibility between a point-like electron and finite mass.     

分段均匀弦的Casimir能量

Casimir能量可看成是由于边界的出现、时空的弯曲以及某些背景场的存在而引起的量子场真空能量极化.由于对Casimir能量的研究能加深对量子场本质的了解,近来对它的研究兴趣正在增加.Brevik等人首先讨论了分段均匀弦的Casiwhr能量.但他们只讨论了闭玻色弦的Casimir能量.本文推广到开和闭的玻色弦,以及费米子弦情形.并且对超弦的Casimir能量也作了探讨.     

Weak Gravitational Field and Casimir Energy

In this paper we consider the effect of a weak gravitation field on the Casimir energy. Under a weak perturbation of a metric, we first obtain the linear energy-momentum tensor of a scalar field in a generic background and then the corrected energy of a scalar filed which satisfies the Dirichlet boundary condition is calculated up to first order of the metric perturbation. We show that our results coincide to the previous related works e.g., the Casimir effect when studied in Fermi coordinates.     

Implicit Versus Explicit Renormalization of the NN Force: An S-Wave Toy Model

We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.     

On the Casimir effect without cutoff

The formulation of the Casimir effect without cutoffs is discussed. Our derivation emphasizes the decisive role of the free-space electromagnetic energy density. The zero point energy arises as an energy per unit volume, i.e., as local (in x space) energy density. It is given by the vaccum expectation value of the free-space Hamiltonian density in the Fock representation corresponding to the non-trivial geometry. The two Fock representations corresponding to the system with and without plates are proved to be inequivalent.     

On the Renormalization of Feynman Integrals

An arbitrary Feynman integral is considered for external momenta in the Euclidean region, the usual rotation of energy contours having been used to write the integral as an integral over Euclidean internal momenta. A compactification of the space of internal momenta is defined, and the Feynman integral is written as the integral of a current on this compact manifold. This presentation of the integral is used to give a proof of the convergence criterion for Feynman integrals, and to show that a well-defined renormalized integral may be obtained by a subtraction operation or by analytic renormalization.     

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent α > 1 of certain monotone combinatorial types. We prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated two-dimensional strong unstable manifold. For monotone families of Lorenz maps we prove that each infinitely renormalizable combinatorial type has a unique representative within the family. We also prove that each infinitely renormalizable map has no wandering intervals, is ergodic, and has a uniquely ergodic minimal Cantor attractor of measure zero.     

On a theory of the Casimir effect

We develop a mathematically precise framework for the Casimir effect. A major role is played by Dietz's idea of identifying the Casimir energy as the regularization-independent Ramanujan sum of an asymptotic series. As an illustration, we treat two cases: parallel plates and the sphere. We finally discuss the open problem of the Casimir force for the cube. We propose an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive sign of the force.     

Renormalization Conditions and the Sliding Scale in the Implicit Regularization Scheme: A Simple Connection

We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the calculation, the introduction of a mass scale is a direct consequence of a set of renormalization conditions. As an illustration the one-loop -function for QED and ⁴ theories are derived. They are given in terms of derivatives of appropriately systematized functions (related to definite parts of the amplitudes) with respect to a mass scale . Our formal scheme can be easily generalized for higher loop calculations.     

On the shape dependence of the tangential Casimir force

The normal and tangential Casimir force for the rack gear is calculated numerically in the case of ideal boundary conditions for the electromagnetic field—perfect reflection on the boundaries. The resulting tangential force appears to be essentially shape-dependent. Relatively small shape variations lead to the essential changes in tangential force, whereas normal force remains almost unchanged.     

On Schwinger's method for obtaining the Casimir effect

We show that a slight modification in Schwinger's method leads directly to the finite result for the Casimir energy of a massless scalar theory.     

Weak Gravitational Wave and Casimir Energy of a Scalar Field

In this paper, we calculate the effect of a weak gravitational field on the Casimir force between two ideal plates subjected to a massless minimally coupled field. It is the aim of this work to study the Casimir energy under a weak perturbation of gravity. Moreover, the fluctuations of the stress-energy tensor for a scalar field in de Sitter space-time are computed as well.     

Casimir Energy of an Open String with Angle-Dependent Boundary Conditions

Journal of Experimental and Theoretical Physics - We consider an open string with ends laying on the two different solid beams (rods). This setup is equivalent to two scalar fields with a set of...     

Spin-P honon Renormalization of the Excitation Energy in a Diluted Two-Dimensional Ferromagnet

The contribution of spin-lattice coupling to the phonon self-energy is calculated for a diluted two-dimensional "soft" ferromagnet. The calculations are based on a bond percolation model. Numerical results are presented for the dampings of phonon excitations. At low temperature, the damping rate is much smaller than the frequency of excitations, leading to well-defined phonons. The overall features of the Г ( q ) curves possess similar characteristics: Г ( q ) has two maximum points at qa ≈ 0.5 and qa ≈ 1.7, the value of the latter is much larger than the former. The temperature-dependent phonon line widths arising from spinlattice coupling are also presented. We point out the sensitivity of the interaction on bond concentration of the network.     

On the Relation Between Casimir Forces and Bulk Correlations

Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.