相关论文: Loop and Path Spaces and Four-Dimensional BF Theor…

In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional…

We use the Van Vleck-Primas perturbation theory to study the problem of parallel transport of the eigenvectors of a parameter-dependent Hamiltonian. The perturbative approach allows us to define a non-Abelian connection $\mathcal{A}$ that…

This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a ``free'' model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution…

Quantum physics in flat-band (FB) systems embodies a variety of exotic phenomenon and even counter intuitive features. The quantum transport in several graphene based compounds that exhibit a flat band and a tunable gap is investigated.…

We study large N dualities for a general class of N=1 theories realized on type IIB D5 branes wrapping 2-cycles of local Calabi-Yau threefolds or as effective field theories on D4 branes in type IIA brane configurations. We completely solve…

Let F be a smooth real manifold with a linear connection in the tangent bundle. How can we extend the coefficients of the connection to bi-differential operators that incorporate the original structure at zero order? Take a constant mapping…

A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and…

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…

We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a $n$-fold degenerate eigenspace of a family of Hamiltonians parametrized by…

We study the generic behavior of Hamiltonian trajectories on a regular level set in the cotangent bundle, after projection to the base. We prove that for a generic submersive level set, projected trajectories have discrete…

F-theoretic constructions can alternatively be understood as consequences of certain N = 2 Seiberg-Witten theories via type IIB r D3s probing the quantum corrected orientifold backgrounds. We present four models that come out from such…

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…

The study of vector-like spectra in 4-dimensional F-theory compactifications involves root bundles, which are important for understanding the Quadrillion F-theory Standard Models (F-theory QSMs) and their potential implications in physics.…

Let G be a Lie group. On the trivial principal G-bundle over the Lie algebra of G there is a natural connection whose curvature is the Lie bracket. The exponential map is given by parallel transport of this connection. If G is the…

We generalize our picture in [arXiv:0904.1744], and consider a pure abelian gauge theory on a four-manifold with nonlocal operators of every codimension arbitrarily and simultaneously inserted. We explicitly show that (i) the theory enjoys…

There exists a simple rule by which path integrals for the motion of a point particle in a flat space can be transformed correctly into those in curved space. This rule arose from well-established methods in the theory of plastic…

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + \alpha x^2, for example . The space coordinate is continued to a complex plane and the connection…

Given a principal $G$-bundle $P \to M$ and two $C^1$ curves in $M$ with coinciding endpoints, we say that the two curves are holonomically equivalent if the parallel transport along them is identical for any smooth connection on $P$. The…

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…