58 research outputs found
Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature
We propose a two-step procedure to study the order of phase transitions at
finite temperature in electroweak theory and in simplified models thereof. In a
first step a coarse grained free energy is computed by perturbative methods. It
is obtained in the form of a 3-dimensional perfect lattice action by a block
spin transformation. It has finite temperature dependent coefficients. In this
way the UV-problem and the infrared problem is separated in a clean way. In the
second step the effective 3-dimensional lattice theory is treated in a
nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap
equation), by real space renormalization group methods, or by computer
simulations. In this paper we outline the principles for -theory
and scalar electrodynamics. The Ba{\l}aban-Jaffe block spin transformation for
the gauge field is used. It is known how to extend this transformation to the
nonabelian case, but this will not be discussed here.Comment: path to figures (in added uu-file) revised, no other changes 33
pages, 3 figures, late
Blockspin transformation for finite temperature field theories with gauge fields
A procedure is proposed to study QFT at zero or at finite temperature by a
sequence of real space renormalization group (RG) or blockspin transformations.
They transform to effective theories on coarser and coarser lattices.The
ultimate aim is to compute constraint effective potentials, i.e. the free
energy as a function of suitable order parameters.From the free energy one can
read off the thermodynamic behaviour of the theory, in particular the existence
and nature of phase transitions. In a finite temperature QFT one begins with
either one or a sequence of transformations which transform the original theory
into an effective theory on a three-dimensional lattice. Its effective action
has temperature dependent coefficients. Thereafter one may proceed with further
blockspin transformations of the three-dimensional theory. Assuming a finite
volume, this can in principle be continued until one ends with a lattice with a
single site. Its effective action is the constraint effective potential. In
each RG-step, an integral over the high frequency part of the field has to be
performed. This is done perturbatively and requires the knowledge of bare
fluctuation field propagators and of interpolation operators which enter into
the vertices. A detailed examination of these quantities is presented for
scalar fields, abelian gauge fields and for Higgs fields, finite temperature is
admitted.Comment: 88 pages, latex, 17 figures appende
A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature
We propose the study of the phase transition in the scalar electroweak theory
at finite temperature by a two - step method. It combines i) dimensional
reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin
transformation, and ii) either further real space renormalization group
transformations, or solution of gap equations, for the 3d lattice theory. A gap
equation can be obtained by using the Peierls inequality to find the best
quadratic approximation to the 3d action. % This method avoids the lack of self
consistency of the usual treatments which do not separate infrared and
UV-problems by introduction of a lattice cutoff. The effective 3d lattice
action could also be used in computer simulations.Comment: 3 pages, LaTeX file, contribution to Lattice 9
Nonperturbative Evolution Equation for Quantum Gravity
A scale--dependent effective action for gravity is introduced and an exact
nonperturbative evolution equation is derived which governs its renormalization
group flow. It is invariant under general coordinate transformations and
satisfies modified BRS Ward--Identities. The evolution equation is solved for a
simple truncation of the space of actions. In 2+epsilon dimensions,
nonperturbative corrections to the beta--function of Newton's constant are
derived and its dependence on the cosmological constant is investigated. In 4
dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's
constant increases at large distances.Comment: 35 pages, late
Hochschule als „offener“ Bildungskontext für lebenslanges Lernen? Befunde und Perspektiven für die empirische (Weiter-)Bildungsforschung
Thermal variational principle and gauge fields
A Feynman-Jensen version of the thermal variational principle is applied to
hot gauge fields, Abelian as well as non-Abelian: scalar electrodynamics
(without scalar self-coupling) and the gluon plasma. The perturbatively known
self-energies are shown to derive by variation from a free quadratic
(''Gaussian'') trial Lagrangian. Independence of the covariant gauge fixing
parameter is reached (within the order studied) after a reformulation of
the partition function such that it depends on only even powers of the gauge
field. Also static properties (Debye screening) are reproduced this way. But
because of the present need to expand the variational functional, the method
falls short of its potential nonperturbative power.Comment: 36 pages, LaTeX, no figures. Updated version: new title, section on
static properties and some references adde
Perfect three-dimensional lattice actions for four-dimensional quantum field theories at finite temperature
We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here
Blockspin transformations for finite temperature field theories with gauge fields
A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(96-164) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
- …