2,436 research outputs found
Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
We prove an equivalence, in the large N limit, between certain U(N) gauge
theories containing adjoint representation matter fields and their orbifold
projections. Lattice regularization is used to provide a non-perturbative
definition of these theories; our proof applies in the strong coupling, large
mass phase of the theories. Equivalence is demonstrated by constructing and
comparing the loop equations for a parent theory and its orbifold projections.
Loop equations for both expectation values of single-trace observables, and for
connected correlators of such observables, are considered; hence the
demonstrated non-perturbative equivalence applies to the large N limits of both
string tensions and particle spectra.Comment: 40 pages, JHEP styl
From Instantons to Sphalerons: Time-Dependent Periodic Solutions of SU(2)-Higgs Theory
We solve numerically for periodic, spherically symmetric, classical solutions
of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of
short periods the solutions approach tiny instanton-anti-instanton
superpositions while, for longer periods, the solutions merge with the static
sphaleron. A previously predicted bifurcation point, where two branches of
periodic solutions meet, appears for Higgs boson masses larger than .Comment: 14 pages, RevTeX with eps figure
N-dimensional electron in a spherical potential: the large-N limit
We show that the energy levels predicted by a 1/N-expansion method for an
N-dimensional Hydrogen atom in a spherical potential are always lower than the
exact energy levels but monotonically converge towards their exact eigenstates
for higher ordered corrections. The technique allows a systematic approach for
quantum many body problems in a confined potential and explains the remarkable
agreement of such approximate theories when compared to the exact numerical
spectrum.Comment: 8 pages, 1 figur
One-Loop Quantum Energy Densities of Domain Wall Field Configurations
We discuss a simple procedure for computing one-loop quantum energies of any
static field configuration that depends non-trivially on only a single spatial
coordinate. We specifically focus on domain wall-type field configurations that
connect two distinct minima of the effective potential, and may or may not be
the solutions of classical field equations. We avoid the conventional summation
of zero-point energies, and instead exploit the relation between functional
determinants and solutions of associated differential equations. This approach
allows ultraviolet divergences to be easily isolated and extracted using any
convenient regularization scheme. Two examples are considered: two-dimensional
theory, and three-dimensional scalar electrodynamics with spontaneous
symmetry breaking at the one-loop level.Comment: RevTex, 29 pages, 1 figure, minor corrections, references adde
An improved time-dependent Hartree-Fock approach for scalar \phi^4 QFT
The model in a finite volume is studied within a
non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of
equilibrium, with particular attention to the structure of the ground state and
of certain dynamical features in the broken symmetry phase. The mean-field
coupled time-dependent Schroedinger equations for the modes of the scalar field
are derived and the suitable procedure to renormalize them is outlined. A
further controlled gaussian approximation of our tdHF approach is used in order
to study the dynamical evolution of the system from non-equilibrium initial
conditions characterized by a uniform condensate. We find that, during the slow
rolling down, the long-wavelength quantum fluctuations do not grow to a
macroscopic size but do scale with the linear size of the system, in accordance
with similar results valid for the large approximation of the O(N) model.
This behavior undermines in a precise way the gaussian approximation within our
tdHF approach, which therefore appears as a viable mean to correct an unlikely
feature of the standard HF factorization scheme, such as the so-called
``stopping at the spinodal line'' of the quantum fluctuations. We also study
the dynamics of the system in infinite volume with particular attention to the
asymptotic evolution in the broken symmetry phase. We are able to show that the
fixed points of the evolution cover at most the classically metastable part of
the static effective potential.Comment: Accepted for publication on Phys. Rev.
On Axially Symmetric Solutions in the Electroweak Theory
We present the general ansatz, the energy density and the Chern-Simons charge
for static axially symmetric configurations in the bosonic sector of the
electroweak theory. Containing the sphaleron, the multisphalerons and the
sphaleron-antisphaleron pair at finite mixing angle, the ansatz further allows
the construction of the sphaleron and multisphaleron barriers and of the
bisphalerons at finite mixing angle. We conjecture that further solutions
exist.Comment: 17 pages, latex, THU-94/0
Body Fixed Frame, Rigid Gauge Rotations and Large N Random Fields in QCD
The "body fixed frame" with respect to local gauge transformations is
introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied
for static and dynamic quarks. Possible choices of the rigid gauge field
configuration corresponding to a nonvanishing static colormagnetic field in the
"body fixed" frame are discussed. A gauge invariant variational equation is
derived in this frame. For large number N of colors the rigid gauge field
configuration is regarded as random with maximally random probability
distribution under constraints on macroscopic--like quantities. For the uniform
magnetic field the joint probability distribution of the field components is
determined by maximizing the appropriate entropy under the area law constraint
for the Wilson loop. In the quark sector the gauge invariance requires the
rigid gauge field configuration to appear not only as a background but also as
inducing an instantaneous quark-quark interaction. Both are random in the large
N limit.Comment: 29 pages LATEX, Weizmann Institute preprint WIS-93/40/Apr -P
Wigner--Dyson statistics for a class of integrable models
We construct an ensemble of second--quantized Hamiltonians with two bosonic
degrees of freedom, whose members display with probability one GOE or GUE
statistics. Nevertheless, these Hamiltonians have a second integral of motion,
namely the boson number, and thus are integrable. To construct this ensemble we
use some ``reverse engineering'' starting from the fact that --bosons in a
two--level system with random interactions have an integrable classical limit
by the old Heisenberg association of boson operators to actions and angles. By
choosing an --body random interaction and degenerate levels we end up with
GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur
Some New/Old Approaches to QCD
This is a talk delivered at the Meeting on Integrable Quantum Field Theories,
Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent
attempts to revive two old ideas regarding an analytic approach to QCD-the
development of a string representation of the theory and the large N limit of
QCD.Comment: 20 page
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