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 $N>N_c=36/\pi^3\approx 1.161$, where $N$ is the number of fermion replica. For $N<N_c$, 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 $N\to N_c^-$. 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 $1/\alpha_{\rm c}$. 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 $1/\ln L$.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 $q^\mu(\tau)$ 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 $q^\mu(\tau)\to q'^\mu(\tau)$ introduces subtleties in the definition and treatment of the path average $q_0^\mu$, 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