8,701 research outputs found
Effective average action in statistical physics and quantum field theory
An exact renormalization group equation describes the dependence of the free
energy on an infrared cutoff for the quantum or thermal fluctuations. It
interpolates between the microphysical laws and the complex macroscopic
phenomena. We present a simple unified description of critical phenomena for
O(N)-symmetric scalar models in two, three or four dimensions, including
essential scaling for the Kosterlitz-Thouless transition.Comment: 34 pages,5 figures,LaTe
Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
The functional equation governing the renormalization flow of fermionic field
theories is investigated in dimensions without introducing auxiliary
Bose-fields on the example of the Gross-Neveu and the Nambu--Jona-Lasinio
model. The UV safe fixed points and the eigenvectors of the renormalization
group equations linearized around them are found in the local potential
approximation. The results are compared carefully with those obtained with
partial bosonisation. The results do not receive any correction in the
next-to-leading order approximation of the gradient expansion of the effective
action.Comment: extended version to appear in EPJC, 15 pages, 4 figures, uses svjour
WZNW Models from Non-Standard Bilinear Forms
We study the WZNW models based on nonstandard bilinear forms. We approach the
problem from algebraic, perturbative and functional exact methods. It is shown
that even in the case of integer we can find irrational CFT's. We prove
that when the base group is noncompact with nonabelian maximal compact
subgroup, the Kac-Moody representations are nonunitary.Comment: LaTeX file, 26 page
Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
We review the use of an exact renormalization group equation in quantum field
theory and statistical physics. It describes the dependence of the free energy
on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative
solutions follow from approximations to the general form of the coarse-grained
free energy or effective average action. They interpolate between the
microphysical laws and the complex macroscopic phenomena. Our approach yields a
simple unified description for O(N)-symmetric scalar models in two, three or
four dimensions, covering in particular the critical phenomena for the
second-order phase transitions, including the Kosterlitz-Thouless transition
and the critical behavior of polymer chains. We compute the aspects of the
critical equation of state which are universal for a large variety of physical
systems and establish a direct connection between microphysical and critical
quantities for a liquid-gas transition. Universal features of first-order phase
transitions are studied in the context of scalar matrix models. We show that
the quantitative treatment of coarse graining is essential for a detailed
estimate of the nucleation rate. We discuss quantum statistics in thermal
equilibrium or thermal quantum field theory with fermions and bosons and we
describe the high temperature symmetry restoration in quantum field theories
with spontaneous symmetry breaking. In particular, we explore chiral symmetry
breaking and the high temperature or high density chiral phase transition in
quantum chromodynamics using models with effective four-fermion interactions.Comment: 178 pages, appears in Physics Report
The Energy-Momentum Tensor(s) in Classical Gauge Theories
We give an introduction to, and review of, the energy-momentum tensors in
classical gauge field theories in Minkowski space, and to some extent also in
curved space-time. For the canonical energy-momentum tensor of non-Abelian
gauge fields and of matter fields coupled to such fields, we present a new and
simple improvement procedure based on gauge invariance for constructing a gauge
invariant, symmetric energy-momentum tensor. The relationship with the
Einstein-Hilbert tensor following from the coupling to a gravitational field is
also discussed.Comment: 34 pages; v2: Slightly expanded version with some improvements of
presentation; Contribution to Mathematical Foundations of Quantum Field
Theory, special issue in memory of Raymond Stora, Nucl. Phys.
Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
The physics of low-energy quasi-particle excitations in disordered d-wave
superconductors is a subject of ongoing intensive research. Over the last
decade, a variety of conceptually and methodologically different approaches to
the problem have been developed. Unfortunately, many of these theories
contradict each other, and the current literature displays a lack of consensus
on even the most basic physical observables. Adopting a symmetry-oriented
approach, the present paper attempts to identify the origin of the disagreement
between various previous approaches, and to develop a coherent theoretical
description of the different low-energy regimes realized in weakly disordered
d-wave superconductors. We show that, depending on the presence or absence of
time-reversal invariance and the microscopic nature of the impurities, the
system falls into one of four different symmetry classes. By employing a
field-theoretical formalism, we derive effective descriptions of these
universal regimes as descendants of a common parent field theory of
Wess-Zumino-Novikov-Witten type. As well as describing the properties of each
universal regime, we analyse a number of physically relevant crossover
scenarios, and discuss reasons for the disagreement between previous results.
We also touch upon other aspects of the phenomenology of the d-wave
superconductor such as quasi-particle localization properties, the spin quantum
Hall effect, and the quasi-particle physics of the disordered vortex lattice.Comment: 42 Pages, 8 postscript figures, published version with updated
reference
Group field theories
Group field theories are particular quantum field theories defined on D
copies of a group which reproduce spin foam amplitudes on a space-time of
dimension D. In these lecture notes, we present the general construction of
group field theories, merging ideas from tensor models and loop quantum
gravity. This lecture is organized as follows. In the first section, we present
basic aspects of quantum field theory and matrix models. The second section is
devoted to general aspects of tensor models and group field theory and in the
last section we examine properties of the group field formulation of BF theory
and the EPRL model. We conclude with a few possible research topics, like the
construction of a continuum limit based on the double scaling limit or the
relation to loop quantum gravity through Schwinger-Dyson equationsComment: Lectures given at the "3rd Quantum Gravity and Quantum Geometry
School", march 2011, Zakopan
- …