相关论文: Orbifold Quantum Cohomology

Quantum probability theory and complex analysis for children.

This paper provides a novel metametaphysical approach to quantum indeterminacy. More specifically, it argues that bivalent quantum logic can successfully account for this kind of indeterminacy, given the non-truth-functional character of…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

In this brief review we describe the idea of holonomic quantum computation. The idea of geometric phase and holonomy is introduced in a general way and we provide few examples that should help the reader understand the issues involved.

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

An overview of the accomplishments of constructive quantum field theory is provided.

The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…

As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a…

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

This paper extends the Bohr-Sommerfeld quantization of the spherical pendulum to a full quantum theory. This the first application of geometric quantization to a classical system with monodromy.

Universal quantum filter (UQF) is introduced and proved to exist. Optical realization of UQF is proposed in experiment.

The answers on the current status and future development of Quantum Science and Technology are presented.

This is a survey on coarse geometry with an emphasis on coarse homology theories.

The marriage of machine learning and quantum physics may give birth to a new research frontier that could transform both.

In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…

The present paper is mainly a survey of our work arXiv:0708.4221 and arXiv:0808.2440 but it also contains the announcement of some new results. Its main purpose is to present an accessible introduction to a technique allowing efficient…

This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.

We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…

This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.

Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of…