1,917 research outputs found
Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
Compact quantum electrodynamics in 2+1 dimensions often arises as an
effective theory for a Mott insulator, with the Dirac fermions representing the
low-energy spinons. An important and controversial issue in this context is
whether a deconfinement transition takes place. We perform a renormalization
group analysis to show that deconfinement occurs when , where is the number of fermion replica. For , however, there
are two stable fixed points separated by a line containing a unstable
non-trivial fixed point: a fixed point corresponding to the scaling limit of
the non-compact theory, and another one governing the scaling behavior of the
compact theory. The string tension associated to the confining interspinon
potential is shown to exhibit a universal jump as . Our results
imply the stability of a spin liquid at the physical value N=2 for Mott
insulators.Comment: 4 pages; 1 figure; v4: version accepted for publication in PRL.
Additional material: the detailed derivation of the RG equations appearing in
this preprint can be downloaded from
http://www.physik.fu-berlin.de/~nogueira/cqed3.htm
Comment on Path Integral Derivation of Schr\"odinger Equation in Spaces with Curvature and Torsion
We present a derivation of the Schr\"odinger equation for a path integral of
a point particle in a space with curvature and torsion which is considerably
shorter and more elegant than what is commonly found in the literature.Comment: LaTeX file in sr
Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor
The lecture explains the geometric basis for the recently-discovered
nonholonomic mapping principle which specifies certain laws of nature in
spacetimes with curvature and torsion from those in flat spacetime, thus
replacing and extending Einstein's equivalence principle. An important
consequence is a new action principle for determining the equation of motion of
a free spinless point particle in such spacetimes. Surprisingly, this equation
contains a torsion force, although the action involves only the metric. This
force changes geodesic into autoparallel trajectories, which are a direct
manifestation of inertia. The geometric origin of the torsion force is a
closure failure of parallelograms. The torsion force changes the covariant
conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm
Spaces with torsion from embedding and the special role of autoparallel trajectories
As a contribution to the ongoing discussion of trajectories of spinless
particles in spaces with torsion we show that the geometry of such spaces can
be induced by embedding their curves in a euclidean space without torsion.
Technically speaking, we define the tangent (velocity) space of the embedded
space imposing non-holonomic constraints upon the tangent space of the
embedding space. Parallel transport in the embedded space is determined as an
induced parallel transport on the surface of constraints. Gauss' principle of
least constraint is used to show that autoparallels realize a constrained
motion that has a minimal deviation from the free, unconstrained motion, this
being a mathematical expression of the principle of inertia.Comment: LaTeX file in src, no figures. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re259/preprint.htm
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
Decrumpling membranes by quantum effects
The phase diagram of an incompressible fluid membrane subject to quantum and
thermal fluctuations is calculated exactly in a large number of dimensions of
configuration space. At zero temperature, a crumpling transition is found at a
critical bending rigidity . For membranes of fixed lateral
size, a crumpling transition occurs at nonzero temperatures in an auxiliary
mean field approximation. As the lateral size L of the membrane becomes large,
the flat regime shrinks with .Comment: 9 pages, 4 figure
Perturbatively Defined Effective Classical Potential in Curved Space
The partition function of a quantum statistical system in flat space can
always be written as an integral over a classical Boltzmann factor \exp[
-\beta V^{\rm eff cl({\bf x}_0)], where V^{\rm eff cl({\bf x}_0) is the
so-called effective classical potential containing the effects of all quantum
fluctuations. The variable of integration is the temporal path average {\bf
x_0\equiv \beta ^{-1}\int_0^ \beta d\tau {\bf x}(\tau). We show how to
generalize this concept to paths in curved space with metric
g_{\mu \nu (q), and calculate perturbatively the high-temperature expansion
of V^{\rm eff cl(q_0). The requirement of independence under coordinate
transformations introduces subtleties in the
definition and treatment of the path average , and covariance is
achieved only with the help of a suitable Faddeev-Popov procedure.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/33
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