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J. Froehlich

Publications and source records attributed to J. Froehlich.

33 records · Page 2Linked to original sources
arXiv2000

Asymptotic Electromagnetic Fields in Models of Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results yield some mathematically rigorous understanding of Rayleigh scattering and of the phenomenon of relaxation of isolated atoms to their ground states. Our proofs are based on propagation estimates for electrons inspired by similar estimates known from $N$-body scattering theory.

math-ph↗
arXiv2000

Universality in Quantum Hall Systems: Coset Construction of Incompressible States

Incompressible Quantum Hall fluids (QHF's) can be described in the scaling limit by three-dimensional topological field theories. Thanks to the correspondence between three-dimensional topological field theories and two dimensional chiral conformal field theories (CCFT's), we propose to study QHF's from the point of view of CCFT's. We derive consistency conditions and stability criteria for those CCFT's that can be expected to describe a QHF. A general algorithm is presented which uses simple currents to construct interesting examples of such CCFT's. It generalizes the description of QHF's in terms of Quantum Hall lattices. Explicit examples, based on the coset construction, provide candidates for the description of Quantum Hall fluids with Hall conductivity s_H=1/2 e^2/h, 1/4 e^2/h, 3/5 e^2/h, e^2/h,...

cond-mat.mes-hall↗
arXiv1999

Fundamental strings in Dp-Dq brane systems

We study conformal field theory correlation functions relevant for string diagrams with open strings that stretch between several parallel branes of different dimensions. In the framework of conformal field theory, they involve boundary condition changing twist fields which intertwine between Neumann and Dirichlet conditions. A Knizhnik-Zamolodchikov-like differential equation for correlators of such boundary twist fields and ordinary string vertex operators is derived, and explicit integral formulas for its solutions are provided.

hep-th↗
arXiv1999

On the extended nature of edge states of Quantum Hall Hamiltonians

Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas - so-called edge states - are studied. For finite samples it is shown that edge states with energy in an appropriate range between Landau levels remain extended along the boundary in the presence of a small amount of disorder, in the sense that they carry a non-zero chiral edge current. For a two-dimensional electron gas confined to a half-plane, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states.

math-ph↗
arXiv1998

Supersymmetric quantum theory and non-commutative geometry

Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.

math-ph↗
arXiv1998

Gauge-invariant charged, monopole and dyon fields in gauge theories

We propose explicit recipes to construct the euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed.

hep-th↗
arXiv1997

Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995

This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what supersymmetric quantum theory teaches us about differential topology and geometry. Non-commutative differential topology and geometry are developed in some detail. As an example, the non-commutative torus is studied. An introduction to string theory and $M$(atrix) models is provided, and it is outlined how tools of non-commutative geometry can be used to explore the geometry of string theory and conformal field theory.

hep-th↗
arXiv1997

On Zero-Mass Ground States in Super-Membrane Matrix Models

We recall a formulation of super-membrane theory in terms of certain matrix models. These models are known to have a mass spectrum given by the positive half-axis. We show that, for the simplest such matrix model, a normalizable zero-mass ground state does not exist.

hep-th↗
arXiv1996

Supersymmetric quantum theory and (non-commutative) differential geometry

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Replacing commutative algebras of functions by non-commutative *-algebras of operators, while retaining supersymmetry, we arrive at a formulation of non-commutative geometry encompassing and extending Connes' original approach. We explore different types of non-commutative geometry and introduce notions of non-commutative manifolds and non-commutative phase spaces. One of the main motivations underlying our work is to construct mathematical tools for novel formulations of quantum gravity, in particular for the investigation of superstring vacua.

hep-th↗
arXiv1995

Renormalization Group Methods: Landau-Fermi Liquid and BCS Superconductor

This is the second part of the notes to the course on quantum theory of large systems of non-relativistic matter taught by J. Fröhlich at the 1994 Les Houches summer school. It is devoted to a sketchy exposition of some of the beautiful and important, recent results of J.Feldman and E.Trubowitz, and J. Feldman, H. Knörrer, D. Lehmann, J. Magnen, V. Rivasseau and E. Trubowitz. Their results are about a mathematical analysis of non-relativistic many-body theory, in particular of the Landau-Fermi liquid and BCS superconductivity, using Wilson's renormalization group methods and the techniques of the $1/N$-expansion. While their work is ultimately aimed at a complete mathematical control (beyond perturbative expansions) of systems of weakly coupled electron gases at positive density and small or zero temperature, we can only illustrate some of their ideas within the context of perturbative solutions of Wilson-type renormalization group flow equations (we calculate leading-order terms in a $1/N$-expansion, where $N$ is an energy scale) and of one-loop effective potential calculations of the BCS superconducting ground state. Contents: 1. Background material 2. Weakly coupled electron gases 3. The renormalization group flow 4. Spontaneous breaking of gauge invariance, and superconductivity

cond-mat↗
arXiv1995

Quantum Theory of Large Systems of Non-Relativistic Matter

1. Introduction 2. The Pauli Equation and its Symmetries {2.1} Gauge-Invariant Form of the Pauli Equation {2.2} Aharonov-Bohm Effect {2.3} Aharonov-Casher Effect 3. Gauge Invariance in Non-Relativistic Quantum Many-Particle Systems {3.1} Differential Geometry of the Background {3.2} Systems of Spinning Particles Coupled to External Electromagnetic and Geometric Fields {3.3} Moving Coordinates and Quantum-Mechanical Larmor Theorem 4. Some Key Effects Related to the $U(1) \times SU(2)$ Gauge Invariance of Non-Relativistic Quantum Mechanics {4.1} ``Tidal'' Aharonov-Bohm and ``Geometric'' Aharonov-Casher Effects {4.2} Flux Quantization {4.3} Barnett and Einstein-deHaas Effects {4.4} Meissner-Ochsenfeld Effect and London Theory of Superconductivity {4.5} Quantum Hall Effect 5. Scaling Limit of the Effective Action of Fermi Systems, and Classification of States of Non-Relativistic Matter 6. Scaling Limit of the Effective Action of a Two-Dimensional, Incompressible Quantum Fluid {6.1} Scaling Limit of the Effective Action {6.2} Linear Response Theory and Current Sum Rules {6.3} Quasi-Particle Excitations and a Spin-Singlet Electron Pairing Mechanism 7. Anomaly Cancellation and Algebras of Chiral Edge Currents in Two- Dimensional, Incompressible Quantum Fluids {7.1} Integer Quantum Hall Effect and Edge Currents {7.2} Edge Excitations in Spin-Polarized Quantum Hall Fluids 8. Classification of Incompressible Quantum Hall Fluids {8.1} QH Fluids and QH Lattices: Basic Concepts {8.2} A Dictionary Between the Physics of QH Fluids and the Mathematics of QH Lattices {8.3} Basic Invariants of Chiral QH Lattices (CQHLs) and their Physical Interpretations {8.4} General Theorems and Classification Results for CQHLs {8.5} Maximally Symmetric CQHLs {8.6} Summary and Physical Implications of the Classification Results

cond-mat↗
arXiv1995

STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS

A classification of incompressible quantum Hall fluids in terms of integral lattices and arithmetical invariants thereof is proposed. This classification enables us to characterize the plateau values of the Hall conductivity $\sH$ in the interval $\,(0,1]\,$ (in units where $\,e^2/h=1$) corresponding to ``stable'' incompressible quantum Hall fluids. A bijection, called shift map, between classes of stable incompressible quantum Hall fluids corresponding to plateaux of $\sH$ in the intervals $\,[1/(2\mini p+1),1/(2\mini p-1)\mini)\,$ and $\,[1/(2\mini q+1),1/(2\mini q-1)\mini)$, respectively, is constructed, with $\,p,q=1,2,3, (\ldots),\ p\neq q$. Our theoretical results are carefully compared to experimental data, and various predictions and experimental implications of our theory are discussed.

cond-mat↗
arXiv1995

A CLASSIFICATION OF QUANTUM HALL FLUIDS

In this paper, the key ideas of characterizing universality classes of dissipation-free (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many general theorems about the classification of quantum Hall lattices are stated and their physical implications are discussed. Physically relevant subclasses of quantum Hall lattices are defined and completely classified. The results are carefully compared with experimental data and also with other theoretical schemes (the hierarchy schemes). Several proposals for new experiments are made which could help to settle interesting issues in the theory of the (fractional) quantum Hall effect and thus would lead to a deeper understanding of this remarkable effect.

cond-mat↗
arXiv1994

Bosonization of Fermi Systems in Arbitrary Dimension in Terms of Gauge Forms

We present a general method to bosonize systems of Fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge- and current density in terms of a bosonic antisymmetric tensorfield of a rank d--1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analyzing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such as Wegner -'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London superconductors, etc.. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.

hep-th↗