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.     

Towards a transport theory of the quark-gluon plasma: Infrared divergences and scalar-meson theory

We consider the transport theory of an ultra-relativistic gas of particles. We study infrared divergences which may appear in a naive perturbative treatment in a massless scalar meson theory. We briefly discuss the potential applications of transport theory for ultra-relativistic nuclear collisions.     

Deconstruction of Gravity

We review how one can construct a deconstructed gravity by a transverse latticification of 5D General Relativity. The obtained theory is a multigravity theory, with link fields that are explicitly constructed out of the metric. We also discuss the spectrum of the theory at the level of the linearized theory.     

The T-dual symmetries of a bosonic string

We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world-sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.     

On general properties of Lorentz-invariant formulation of noncommutative quantum field theory

We study general properties of certain Lorentz-invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge causality condition. This is the consequence of the infinite nonlocality of the theory getting spread in all spacetime directions. We also show that the time-ordered perturbation theory arising from the Hamiltonian formulation of noncommutative quantum field theories remains inequivalent to the covariant perturbation theory with usual Feynman rules even after restoration of Lorentz symmetry.     

Chaotic Quantization of Classical Gauge Fields

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and calculate Planck's constant from quantities defined in the underlying classical gauge theory.     

Superconductivity and Temperature Effects on Davydov Model of α-Helix Protein

We study the thermodynamic properties of α-helix protein on the basis of Davydov theory. The Hamiltonian of Davydov theory can be represented as a form of pairing Hamiltonian in the momentum space. We prove that the quasi-classical Davydov theory is essentially a theory with Bose condensation no matter whether the molecular excitations are treated as fermions or bosons. The transition temperature of superconductivity theory gives the existence condition of the Davydov soliton.     

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.     

Phase transitions in systems with a finite number of dominant ground states

We develop a theory of low-temperature phases of discrete lattice systems which is guided by formal perturbation theory, and which in turn yields its rigorous justification. The theory applies to many systems with an infinite number of ground states for which the perturbation theory predicts a finite number of low-temperature phases. We illustrate it on a number of examples.     

A quantum deformation of invariants of binary forms

The modern representation theory has its roots in the classical theory of invariants of binary forms of Caley, Silvester, Clebsch, Gordan, Capelli etc. We use the theory of the quantum group U _q(sl(2, IR) in order to develop a quantum theory of invariants. Higher binary forms are introduced on the basis of braided algebras. We define quantised invariants and give basic examples. We show that the symbolic method of Clebsch and Gordan works also in the quantised case. We calculate the quantised discriminant of the quadratic form, the quantised catalecticant of the quartic form and further invariants without a classical analogon.     

Dynamics of weakly localized waves

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

On the Domain of Applicability of General Relativity

We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue that, as it stands, GR is deficient whether it is treated as a microscopic or a macroscopic theory of gravity. We briefly discuss some recent attempts at removing this shortcoming through the construction of a macroscopic theory of gravity. We point out that such macroscopic extensions of GR are likely to be nonunique and involve non-Riemannian geometrical frameworks.     

Finite-element theory of transport in ferromagnet-normal metal systems

We formulate a theory of spin dependent transport in an electronic circuit involving ferromagnetic elements with noncollinear magnetization which is based on the conservation of spin and charge current. The theory considerably simplifies the calculation of the transport properties of complicated ferromagnet-normal metal systems. We illustrate the theory by considering a novel three-terminal device.     

Interactions of strings and D-branes from M theory

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.     

Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory

We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin–Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.     

The cosmological constant of modular closed string field theory. I

We formulate closed string field theory as a quantum theory of modular geometry. We determine the full interacting quantum hamiltonian to all loop orders in perturbation theory. The free action has a new highly non-linear symmetry acting on the string field, and the kinetic operator. Perturbatively we demonstrate that the new theory gives the correct expression for the cosmological constant that is ultraviolet finite to one-loop order.     

Kochen-Specker Theorem as a Precondition for Quantum Computing

We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or ?1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.