480 research outputs found
A transition in the spectrum of the topological sector of theory at strong coupling
We investigate the strong coupling region of the topological sector of the
two-dimensional theory. Using discrete light cone quantization (DLCQ),
we extract the masses of the lowest few excitations and observe level
crossings. To understand this phenomena, we evaluate the expectation value of
the integral of the normal ordered operator and we extract the number
density of constituents in these states. A coherent state variational
calculation confirms that the number density for low-lying states above the
transition coupling is dominantly that of a kink-antikink-kink state. The
Fourier transform of the form factor of the lowest excitation is extracted
which reveals a structure close to a kink-antikink-kink profile. Thus, we
demonstrate that the structure of the lowest excitations becomes that of a
kink-antikink-kink configuration at moderately strong coupling. We extract the
critical coupling for the transition of the lowest state from that of a kink to
a kink-antikink-kink. We interpret the transition as evidence for the onset of
kink condensation which is believed to be the physical mechanism for the
symmetry restoring phase transition in two-dimensional theory.Comment: revtex4, 14 figure
Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state
A functional integral representation is given for a large class of quantum
mechanical models with a non--L2 ground state. As a prototype the particle in a
periodic potential is discussed: a unique ground state is shown to exist as a
state on the Weyl algebra, and a functional measure (spectral stochastic
process) is constructed on trajectories taking values in the spectrum of the
maximal abelian subalgebra of the Weyl algebra isomorphic to the algebra of
almost periodic functions. The thermodynamical limit of the finite volume
functional integrals for such models is discussed, and the superselection
sectors associated to an observable subalgebra of the Weyl algebra are
described in terms of boundary conditions and/or topological terms in the
finite volume measures.Comment: 15 pages, Plain Te
On Renormalization Group Flows and Polymer Algebras
In this talk methods for a rigorous control of the renormalization group (RG)
flow of field theories are discussed. The RG equations involve the flow of an
infinite number of local partition functions. By the method of exact
beta-function the RG equations are reduced to flow equations of a finite number
of coupling constants. Generating functions of Greens functions are expressed
by polymer activities. Polymer activities are useful for solving the large
volume and large field problem in field theory. The RG flow of the polymer
activities is studied by the introduction of polymer algebras. The definition
of products and recursive functions replaces cluster expansion techniques.
Norms of these products and recursive functions are basic tools and simplify a
RG analysis for field theories. The methods will be discussed at examples of
the -model, the -model and hierarchical scalar field
theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference
``Constructive Results in Field Theory, Statistical Mechanics and Condensed
Matter Physics'', 25-27 July 1994, Palaiseau, Franc
Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
We extend the recently developed kinematical framework for diffeomorphism
invariant theories of connections for compact gauge groups to the case of a
diffeomorphism invariant quantum field theory which includes besides
connections also fermions and Higgs fields. This framework is appropriate for
coupling matter to quantum gravity. The presence of diffeomorphism invariance
forces us to choose a representation which is a rather non-Fock-like one : the
elementary excitations of the connection are along open or closed strings while
those of the fermions or Higgs fields are at the end points of the string.
Nevertheless we are able to promote the classical reality conditions to quantum
adjointness relations which in turn uniquely fixes the gauge and diffeomorphism
invariant probability measure that underlies the Hilbert space. Most of the
fermionic part of this work is independent of the recent preprint by Baez and
Krasnov and earlier work by Rovelli and Morales-Tec\'otl because we use new
canonical fermionic variables, so-called Grassman-valued half-densities, which
enable us to to solve the difficult fermionic adjointness relations.Comment: 26p, LATE
Initial conditions for turbulent mixing simulations
In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much debated question of models for initial conditions and the possible influence of unrecorded long wave length contributions to the instability growth rate α.У контексті класичної гідродинамічної нестійкості Релея - Тейлора вивчено дискусійне питання моделей для початкових умов і можливий вплив незафіксованих далекосяжних вкладів на швидкість росту нестійкості альфа
SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension
We prove that if is the entropy
solution to a strictly hyperbolic system of conservation laws with
genuinely nonlinear characteristic fields then up to a
countable set of times the function is in
, i.e. its distributional derivative is a measure with no
Cantorian part.
The proof is based on the decomposition of into waves belonging to
the characteristic families and the balance
of the continuous/jump part of the measures in regions bounded by
characteristics. To this aim, a new interaction measure \mu_{i,\jump} is
introduced, controlling the creation of atoms in the measure .
The main argument of the proof is that for all where the Cantorian part
of is not 0, either the Glimm functional has a downward jump, or there is
a cancellation of waves or the measure is positive
Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
We study quartic matrix models with partition function Z[E,J]=\int dM
\exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of
Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0
is a scalar coupling constant and the matrix J is used to generate correlation
functions. For E not a multiple of the identity matrix, we prove a universal
algebraic recursion formula which gives all higher correlation functions in
terms of the 2-point function and the distinct eigenvalues of E. The 2-point
function itself satisfies a closed non-linear equation which must be solved
case by case for given E. These results imply that if the 2-point function of a
quartic matrix model is renormalisable by mass and wavefunction
renormalisation, then the entire model is renormalisable and has vanishing
\beta-function.
As main application we prove that Euclidean \phi^4-quantum field theory on
four-dimensional Moyal space with harmonic propagation, taken at its
self-duality point and in the infinite volume limit, is exactly solvable and
non-trivial. This model is a quartic matrix model, where E has for N->\infty
the same spectrum as the Laplace operator in 4 dimensions. Using the theory of
singular integral equations of Carleman type we compute (for N->\infty and
after renormalisation of E,\lambda) the free energy density
(1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear
integral equation. Existence of a solution is proved via the Schauder fixed
point theorem.
The derivation of the non-linear integral equation relies on an assumption
which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae
and vanishing of \beta-function hold for general quartic matrix models. v3:
We add the existence proof for a solution of the non-linear integral
equation. A rescaling of matrix indices was necessary. v2: We provide
Schwinger-Dyson equations for all correlation functions and prove an
algebraic recursion formula for their solutio
A theorem concerning twisted and untwisted partition functions in U(N) and SU(N) lattice gauge theories
In order to get a clue to understanding the volume-dependence of vortex free
energy (which is defined as the ratio of the twisted against the untwisted
partition function), we investigate the relation between vortex free energies
defined on lattices of different sizes. An equality is derived through a simple
calculation which equates a general linear combination of vortex free energies
defined on a lattice to that on a smaller lattice. The couplings in the
denominator and in the numerator however shows a discrepancy, and we argue that
it vanishes in the thermodynamic limit. Comparison between our result and the
work of Tomboulis is also presented. In the appendix we carefully examine the
proof of quark confinement by Tomboulis and summarize its loopholes.Comment: 19 pages, 4 figures; v2:Clarifying comments added; v3:Appendix added,
the version published in Physics Letters
Vanishing of Beta Function of Non Commutative Theory to all orders
The simplest non commutative renormalizable field theory, the model
on four dimensional Moyal space with harmonic potential is asymptotically safe
up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.
Rivasseau. We extend this result to all orders.Comment: 12 pages, 3 figure
Quantum field theory on manifolds with a boundary
We discuss quantum theory of fields \phi defined on (d+1)-dimensional
manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which
is a bilinear form in \phi defines the Gaussian measure with a covariance
(Green function) {\cal G}. We discuss a relation between the quantum field
theory with a fixed boundary condition \Phi and the theory defined by the Green
function {\cal G}. It is shown that the latter results by an average over \Phi
of the first. The QFT in (anti)de Sitter space is treated as an example. It is
shown that quantum fields on the boundary are more regular than the ones on
(anti) de Sitter space.Comment: The version to appear in Journal of Physics A, a discussion on the
relation to other works in the field is adde
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