On second-quantized open superstring theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a “matrix string” model. The theory is defined by the neighborhood of a 1 + 1-dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string endpoints are created and destroyed by a boundary twist operator.     

Simplicial vs. continuum string theory and loop equations

We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory—the theory describing embeddings of two-dimensional simplicial complexes into the spacetime of the matrix field theory. This relation between the loop equations and the simplicial string theory gives further arguments that favor one of the statements of the paper hep-th/0407018. The statement is that there is an equivalence between the partition function of the simplicial string theory and the functional integral in a continuum string theory—the theory describing embeddings of smooth two-dimensional world-sheets into the spacetime of the matrix field theory in question.     

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.     

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.     

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.     

Theory of a gravitational gauge field with localization of the de Sitter group

A de Sitter-invariant gauge theory is formulated for the case where a 40-component de Sitter A-field is present. It is shown that the theory coincides with the Poincare-invariant gauge theory in a space with torsion with a cosmological term. Two other versions of a de Sitter-invariant theory are also discussed: the first is a metric theory of gravitation in a Riemann space; the second is a de Sitter-invariant generalization of the tetrad theory of gravitation in a space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–53, November, 1986.     

Theory Assessment and Final Theory Claim in String Theory

String theory has by now maintained a highly influential position in high energy physics for more than a quarter of a century. The present article analyses the reasons for the considerable trust exponents of string theory have in their theory even though it has neither found empirical confirmation nor a complete formulation up to this point. It is argued that this trust can be understood in terms of an emerging new conception of theory assessment that relies strongly on the identification of limitations to the underdetermination of scientific theory building. The second part of the paper makes the point that another conspicuous element of string theoretical reasoning, the prominent role of the notion of a final theory, can be understood in terms of this altered notion of theory assessment as well.     

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.     

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.     

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.     

Supersymmetry and the Parisi-Sourlas dimensional reduction: A rigorous proof

Functional integrals that are formally related to the average correlation functions of a classical field theory in the presence of random external sources are given a rigorous meaning. Their dimensional reduction to the Schwinger functions of the corresponding quantum field theory in two fewer dimensions is proven. This is done by reexpressing those functional integrals as expectations of a supersymmetric field theory. The Parisi-Sourlas dimensional reduction of a supersymmetric field theory to a usual quantum field theory in two fewer dimensions is proven.Partially supported by the NSF under grant MCS-8301889Partially supported by FAPESP     

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.     

Classical and quantum conformal field theory

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.On leave of absence from the Department of Physics, Weizmann Institute of Science, Rehovot 76100, Israel     

Local State and Sector Theory in Local Quantum Physics

We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can find a condition from which follows automatically the famous DHR selection criterion in DHR-DR theory. As a result, we can understand the condition as consequences of physically natural state preparations in vacuum backgrounds. Furthermore, a theory of orthogonal decomposition of completely positive (CP) maps is developed. It unifies a theory of orthogonal decomposition of states and order structure theory of CP maps. Using it, localized version of sectors is formulated, which gives sector theory for local states with respect to general reference representations.     

On the expansion of a quantum field theory around a topological sector

The idea of treating quantum general relativistic theories in a perturbative expansion around a topological theory has recently received attention, in the quantum gravity literature. We investigate the viability of this idea by applying it to conventional Yang–Mills theory on flat spacetime. This theory admits indeed a formulation as a modified topological theory, like general relativity. We find that the expansion around the topological theory coincides with the usual expansion around the free abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. On the other hand, we point out that the relation of this expansion with the actual quantum BF theory is far from being transparent. Some implications for gravity are discussed.     

Circuit theory for full counting statistics in multiterminal circuits

We propose a theory that treats the current, noise, and, generally, the full current statistics of electron transfer in a mesoscopic system in a unified, simple, and efficient way. The theory appears to be a circuit theory of 2 x 2 matrices associated with Keldysh Green functions. We illustrate the theory by considering the big fluctuations of currents in various three-terminal circuits.     

Scalar-tensor theories of gravitation: Foundations and prospects

A generalization of Einstein's theory is discussed in which the gravitation is described by a tensor and a scalar field. The theory is more consistent with Mach's principle and less reliant on absolute properties of space. The modification involves a violation of the “strong principle of equivalence” on which Einstein's theory is based. In the original version of this new theory, the “constant” of gravitationG is varying and particle masses are fixed. Later on another version of the theory was given in whichG is truly a constant and the particle masses vary. The two versions are related by a conformal transformation. The physical and mathematical foundations of this theory have been discussed and the field equations have been derived. The astrophysical and cosmological consequences of the theory have been elaborately reviewed.     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

Relativistic Single Particle Kinetic Theory

Single particle kinetic theory is the study of the dynamics of a single particle moving through a medium. The only mechanism for change in this theory is through two-body collisions between the single particle and the particles of the medium given by the collision term of Boltzmann's equation in kinetic theory. This article contains a summery of relativistic dynamics and a method of projecting the relativistic dynamical system into phase space. This enables us to express relativistic kinetic theory in terms of phase space variables and also to apply the techniques of approximation in the non-relativistic theory to the relativistic domain.     

Hierarchies of Susy splittings in holographic gauge mediation

We generalize to string theory a construction, originally proposed in field theory, that generates a hierarchy in the splittings between members of super-multiplets in various sectors of the theory.