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.     

Entanglement entropy in Abelian gauge theories

The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z _N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.     

Statistical sums for open and/or oriented strings

The embedding of module spaces of open (with boundaries) and/or non-orientable surfaces into those of closed orientable surfaces is described. This suggests a natural expression of the contributions to statistical sums for bosonic strings in terms of the Mamford measure.     

Open strings from closed strings: Period matrix,measure and ghost determinant

The construction of the double of a surface with boundaries together with an anticonformal involution is used to relate partition functions of closed strings to partition functions of open strings, at an arbitrary order of the perturbation theory. The specific form that the period matrix must have is derived. It is found that the number of components is halved. The partition function factorizes into the product of Neumann and Dirichlet components. In particular, the measure and the ghost determinant factor into two equal components.     

Poisson brackets,strings and membranes

We construct Poisson brackets at the boundaries of open strings and membranes with constant background fields which are compatible with their boundary conditions. The boundary conditions are treated as primary constraints which give infinitely many secondary constraints. We show explicitly that we need only two (the primary one and one of the secondary ones) constraints to determine the Poisson brackets of strings. We apply this to membranes by using canonical transformations. Received: 2 May 2002 / Revised version: 29 May 2002 / Published online: 16 August 2002 RID="a" ID="a" e-mail: tezuka@physics.s.chiba-u.ac.jp     

The Properties of Strings Formed in the Homochiral Solutions of Trifluoroacetylated Amino Alcohols in Cyclohexane

The strings formed in the solutions of trifluoroacetylated amino alcohols in cyclohexane were studied. It was found that microscopic strings with the diameter d ～ 1 μm were woven from tightly coupled rigid submicroscopic strings with the diameter d ～ 0.1 μm in increments of >100 μm. Therefore, the compound strings are transparent, and they usually look like an unstructured cylinder. Microscopic strings can be tightly combined in strings to 60 μm in diameter. Submicroscopic strings are arranged almost parallel to the axis of a microscopic string. The microscopic string acts as a polarizer: it transmits light polarized across its axis and absorbs light polarized along the axis. The majority of these properties can be explained based on the assumption that a connection between the strings of all hierarchical levels in cyclohexane is stronger than that in solvents with different string morphology.     

The gravitational interaction of conical strings

Up to now calculations of the interaction of cosmic strings have neglected gravity. We consider the purely gravitational interactions that occur at large distances, using the conical line singularity for the gravitational field of a string. We construct spaces with multiple intersecting conical strings, that are exactly consistent with General Relativity, and which can be covered in a single Minkowski coordinate patch, using a Regge calculus type construction. We show that after two such strings pass through each other they remain connected by another string, and we derive the branching rules which govern the junction of three strings. These rules apply to conical type strings in any smoothly curved background, whether they are straight or curved, moving or stationary, and they show that, at the junction, the three strings must be as coplanar as is possible in such a space. For these results to be matched onto the short range results of Field Theory calculations, it is suggested that gravitational radiation must be introduced. This would mean that gravitation is not negligible in these interactions.     

Cosmological evolution of monopoles connected by strings

Phase transitions in the early universe can give rise to a system of vacuum strings. Assuming that the strings are topologically stable, it has been recently shown that they can produce density fluctuations which can subsequently lead to galaxy formation. The present paper examines the cosmological evolution of topologically unstable strings. In this case the system consists of strings having monopoles and antimonopoles at the ends, as well as of closed loops. Various physical processes in the system are discussed in detail. It is shown that monopoles and strings disappear long before any appreciable density fluctuations on a galactic scale can be produced.     

On the probability of ferromagnetic strings in antiferromagnetic spin chains

We study the probability of formation of ferromagnetic string in the antiferromagnetic spin-1/2 XXZ chain. We show that in the limit of long strings with weak magnetization per site the bosonization technique can be used to address the problem. At zero temperature the obtained probability is Gaussian as a function of the length of the string. At finite but low temperature there is a crossover from the Gaussian behavior at intermediate lengths of strings to the exponential decay for very long strings. Although the weak magnetization per site is a necessary small parameter justifying our results, the extrapolation of obtained results to the case of maximally ferromagnetic strings is in qualitative agreement with known numerics and exact results. The effect of an external magnetic field on the probability of formation of ferromagnetic strings is also studied.     

Nonsupersymmetric string solitons

We begin a search for nonsupersymmetric/supersymmetric dual string pairs by constructing candidate critical nonsupersymmetric strings as solitons in supersymmetric string theories. Using orbifold techniques, one can construct cosmic string solutions which lie in supersymmetric vacua but which do not fall in supermultiplets. We discuss two three-dimensional examples in detail. The effective worldsheet actions for the soliton strings have (0,2) and (1,1) supersymmetry and the correct numbers of massless bosons and fermions to be critical heterotic and type II strings, respectively.     

Topological order in an exactly solvable 3D spin model

We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R²) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.     

Cosmic strings and domains in unified theories

Unified theories predict that the Universe passes through a sequence of phase transitions as it cools after the big bang. Topological structures (domain walls, strings and monopoles) may be created in these transitions. The production of domains of different zero-temperature vacua (separately by massive walls) excludes some popular scenarios for the breaking of SU(5) and SO(10).Massive strings appear in other schemes. They may be open strings or closed loops. We exhibit an SO(10) example with string formation. SO(8) supergravity may deliver an effective SU(5)× SU(2) unified theory below the Planck mass scale. This can also lead to string production. We present the rather restrictive conditions under which string producing theories are harmless to conventional cosmology. Even then, strings do not seem to provide the initial density perturbations that evolved into galaxies.     

Representation of hysteresis operators for vector-valued inputs by functions on strings

In 1996, Brokate and Sprekels have shown that scalar-valued hysteresis operators for scalar-valued continuous input functions being piecewise monotone can be uniquely represented by functionals defined on the set of all finite alternating strings of real numbers.In this work, it is shown that a similar result can also be derived for hysteresis operators dealing with inputs in a general normed vector space. Considering hysteresis operators defined for continuous inputs that are piecewise monotaffine, it will be shown that these operators can be uniquely represented by functionals acting on an appropriate set of finite strings of elements of this space.     

D-term inflation, cosmic strings, and consistency with cosmic microwave background measurements

Standard D-term inflation is studied in the framework of supergravity. D-term inflation produces cosmic strings; however, it can still be compatible with cosmic microwave background (CMB) measurements without invoking any new physics. The cosmic strings contribution to the CMB data is not constant, nor dominant, contrary to some previous results. Using current CMB measurements, the free parameters (gauge and superpotential couplings, as well as the Fayet-Iliopoulos term) of D-term inflation are constrained.     

Comparison of String Fluid Dynamical Models in General Relativity and Einstein–Cartan theory

Dynamical models of string fluids areconstructed from the general energy-momentum tensor forstring fluids in general relativity and theEinstein-Cartan theories obtained from the Ray-Hilbertvariational principle. Examples of solutions to the fieldequations for general relativistic spacetimes are givenand compared with solutions obtained from the postulatedenergy-momentum tensor of Letelier. Solutions to the field equations in Riemann-Cartanspacetimes are compared with an extended Leteliersolution. All calculations are given for both thestandard and the extended thermodynamics versions inwhich the latter includes the string as thermodynamicvariables. In general relativity, it is shown for blackhole solutions that the general feature of strings(through the string vector) is to produce a shrinkage of the black hole horizon. In RiemannCartanspacetimes, the torsion field equation shows that stringvector can be identified with the torsion vector. Themost striking feature of strings in Riemann-Cartan spacetimes is that in the Reissner-Nordstromsolution, the addition of torsional strings produces thecorrect asympototic behavior of the metric necessary tomatch the experimental galactic rotationcurves.     

Probabilistic estimates of the number of cosmic strings

The dependences of the mean expected number of cosmic strings on their redshift up to the surface of last scattering have been derived. The calculations are based on the geometric probability of a straight string segment crossing a given field and on information about the absence of strings when they are searched for via their gravitational lensing effects in optical catalogs. It is shown that there are no strings for redshifts 0 < z < 1.954, but the expected number of strings for 0 < z < 5 can be no more than 2.1 × 10³ at the 95% confidence level. The expected number of strings for redshifts up to z = 1100 can be no more than 2.4 × 10⁴ at the 95% confidence level. The latter estimate is sensitive to a priori information about the absence of cosmic strings in the redshift range 0 < z < 1.954 in a field of 4.48 square degrees in optical catalogs; it is smaller than the estimate without allowance for this information by 6%.