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In this paper we construct a $(2,2)$ dimensional string theory with manifest $N=1$ spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The…
The theory of {\Gamma}-species is developed to allow species-theoretic study of quotient structures in a categorically rigorous fashion. This new approach is then applied to two graph-enumeration problems which were previously unsolved in…
We find that different asymptotic measurements in quantum field theory can be related to one another through new versions of crossing symmetry. Assuming analyticity, we conjecture generalized crossing relations for multi-particle processes…
The past year has seen enormous progress in string theory. It has become clear that all of the different string theories are different limits of a single theory. Moreover, in certain limits, one obtains a new, eleven-dimensional structure…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
We review the idea of our earlier proposed string field theory \cite{early1,early2,ourappear}, which makes the second quantized string theory appear as described by one or two types of stationary - so called - "objects" for string theories…
It has been shown that there is a sequential embedding structure in a $w_N$\ string theory based on a linearized $W_N$\ algebra. The $w_N$\ string theory is obtained as a special realization of the $w_{N+1}$\ string. The $w_{\infty}$\…
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
In the companion to this paper, we described a generalization of the deterministic quantum cloning process, called enscription, which utilizes entanglement in order to achieve the "copying" of (certain) sets of distinct quantum states which…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
This is the written version of a short talk given at the University of Leipzig in December 1998. It reviews some general aspects of string theory from the viewpoint of the search for an unifying theory. Here, special emphasis lies on the…
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
We discuss the obstacles for defining a set of observable quantities analogous to an S-matrix which are needed to formulate string theory in an accelerating universe. We show that the quintessence models with the equations of state $-1 < w…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…