Two-dimensional topological gravity and intersection theory on the moduli space of holomorphic bundles

We define a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group. This theory is defined in terms of intersection theory on the moduli space of flat connections on a two-dimensional surface and corresponds physically to a two-dimensional reduction and truncation of four-dimensional topological Yang-Mills theory. Two-dimensional topological Yang-Mills theory defines a topological matter system and may be naturally coupled to two-dimensional topological gravity. This topological Yang-Mills theory is also closely related to Chern-Simons gauge theory in 2 + 1 dimensions. We also discuss a relation between SL (2, ) Chern-Simons theory and two-dimensional topological gravity.     

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheim's theory as a perturbation to Tarazona's hard-sphere density functional theory. Each theory approaches Tarazona's theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazona's weighting of Wertheim's theory in the bulk is in good agreement with computer simulation results.     

干涉现象中能量叠加的实验研究

经典的波动理论与量子理论均分别对杨氏双缝干涉实验进行了解释。由于两个解释理论一个简单直观、一个复杂抽象,但两者结果一致,使得学生在学习中容易接受波动理论而排斥量子理论。文中通过实验观测了杨氏双缝干涉光场中能量传递与叠加的实际情况,结果显示实验实际情况与波动理论解释明显不相符合,而与量子理论解释完全相符。通过实验,使学生直观地看到波动理论的局限性,并加深学生对量子力学相关理论的理解。     

The critical supersaturations predicted by nucleation theory

A general set of equations is derived for calculating the supersaturation required to obtain a given rate of nucleation. This set is general enough to encompass all the present theories, the classical theory, the Lothe-Pound theory, the Reiss-Katz-Cohen theory, a recent theory by H. Reiss, and any other theory which includes a size-dependent correction to the classical theory. Comparison of these predictions is made for various substances.     

Bohmian mechanics and quantum field theory

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.     

Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.     

Geometric Formulation of Gauge Theory of Gravity

Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.     

Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation

The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schrödinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory.Partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A8059.     

Scalar-tensor theory and propagating torsion theory

We prove that scalar conformal transformations can convert the variational principle of the propagating torsion theory into the variational principle of general scalar-tensor theory, and show that scalar-tensor theory is conformally equivalent to propagating torsion theory.     

On the relation between Brueckner theory and Jastrow theory of nuclear matter

The two- and three-hole-line contributions to the ground state energy as calculated from Brueckner theory are derived from a cluster expansion followed by variation of the trial function. The implications of that derivation both for Brueckner theory and for Jastrow theory are worked out in detail. It is argued that the Jastrow theory is able to give simpler methods to calculate the ground state energy which may be of the same accuracy as current Brueckner calculations. It is shown that the single-particle potential of Brueckner theory is intimately related to a subsidiary condition used in the variation of the trial function. The main steps which have to be taken in a derivation of the general hole-line expansion from Jastrow theory are indicated. It is shown that the hole-line expansion is not a cluster expansion in the sense of Jastrow theory, and an interpretation is given of the “self-consistent choice” of the single-particle potential advocated in Brueckner theory.     

The properties of conformal blocks,the AGT hypothesis,and knot polynomials

Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern–Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.     

Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)L U(1)Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)L U(1)Y dynamically to U(1)em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.``     

Gravitation and source theory

Schwinger's source theory is applied to the problem of gravitation and its quantization. It is shown that within the framework of a flat-space the source theory implementation leads to a violation of probability. To avoid the difficulty one must introduce a curved space-time hence the source concept may be said to necessitate the transition to a curved-space theory of gravitation. It is further shown that the curved-space theory of gravitation implied by the source theory is not equivalent to the conventional Einstein theory. The source concept leads to a different theory where the gravitational field has a stress-energy tensor t_μ^ν, which contributes to geometric curvatures.     

The bosonization of theories with pseudo-vector interactions

The bosonization of a 2+1 dimensional fermion theory with both vector and pseudo-vector interactions is discussed. This theory describes a fermion field that carries both charge and anomalous magnetic moment. We also consider the bosonization of a fermion theory that contains magnetic moment but no charge. We discuss the relationship of the bosonized theory to the theory that contains Nielsen-Olesen fluxons.     

表面等离子共振效应中传统近似理论与薄膜光学理论

指出Kretschmann模型的传统表面等离子共振公式在求解金属薄膜的参量时存在近似性,采用更为严密的薄膜光学理论,通过薄膜膜系的特征矩阵,得出表面等离子体共振衰减曲线.结果表明,表面等离子体共振近似理论与薄膜光学理论得到的共振角及反射率幅度存在差别;采用等高线图,给出了共振角差随着金属介电常量的变化规律.进一步的实验表明,薄膜光学理论所得模拟结果较表面等离子体共振近似理论与实验值吻合地更好,证明薄膜光学理论应用在表面等离子体共振效应要优于常用的近似理论.最后,采用两种理论对表面等离子体共振传感器进行优化设计,结果表明,两种理论所获得的高灵敏度分布区域差异较大,必须采用薄膜光学理论提供更精确的薄膜参量,来优化设计高灵敏度表面等离子体共振传感器.     

Generalized measure theory

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are given.     

Approximately straight kink theories

A precise meaning is given to the idea of a kink theory approximating a vectoror vector-bundle-valued theory. It is shown that vector theories taking values in a vector bundle with groupSO(n- s,s;), acting naturally, do not approximate any kink theory. It is further shown that, where a kink theory is approximated by a vector bundle theory, the field equations in the vector theory can give rise to field equations in the kink theory. The theory of Skyrme and the sine-Gordon theory are of this form. An example is given of a nonlinear modification of electromagnetism having solitonlike solutions.     

On the Foundations of Superstring Theory

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought. Although it is advertised as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that.     

Effective theory of excitations in a Feshbach-resonant superfluid

A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean-field approximation. Here I develop an effective field theory for the resonant superfluid based on broken symmetry. The theory retains both fermionic quasiparticles and superfluid phonons, the interaction between them being derived nonperturbatively. The theory converges and can be improved order by order, in a manner governed by a low energy expansion rather than by a coupling constant. I apply the effective theory to calculate the specific heat and discuss the theory with a recent heat capacity experiment.