Related papers: Simple Models in Supersymmetric Quantum Mechanics …
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic…
We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann Graphical models (free fermions) defined on the same graph. Calculation of the partition function…
A description is given of how to construct (0,2) supersymmetric conformal field theories as coset models. These models may be used as non-trivial backgrounds for Heterotic String Theory. They are realised as a combination of an anomalously…
A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with…
These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half…
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. They are widely used throughout natural sciences, computational biology and many other fields. Computing the vanishing ideal of the…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
We study fermionic and bosonic systems coupled to a real or synthetic static gauge field that is quantized, so the field itself is a quantum degree of freedom and can exist in coherent superposition. A natural example is electrons on a…
We discuss N=2 supersymmetric quantum mechanics on the lattice using the fermion loop formulation. In this approach the system naturally decomposes into a bosonic and fermionic sector. This allows us to deal with the sign problem arising in…
We construct and analyze unfolded off-shell systems for chiral and vector supermultiplets using multispinor formalism and external currents. We find that auxiliary variables of multispinor formalism allow for the interesting reorganization…
We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…
We study the phases and fixed-point structure of two-dimensional supersymmetric Wess-Zumino models with one supercharge. Our work is based on the functional renormalization group formulated in terms of a manifestly off-shell supersymmetric…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…
We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the…
One considers the quantum dynamics of a charged spin-1/2 particle in an extended external eletromagnetic field that arises from the reduction of a 5-dimensional Abelian gauge theory. The non-relativistic regime of the reduced 4D-dynamics is…
The work aims effective and low-dimensional systems. Some different contexts involving gravitational and electromagnetic interactions are investigated. The electromagnetic one approaches bosonic and fermionic Effective Quantum Field…