6,759 research outputs found
World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
Assuming that at small distances space-time is equivalent to an elastic
medium which is isotropic in space and time directions, we demonstrate that the
quantum nematic liquid arising from this crystal by spontaneous proliferation
of dislocations corresponds with a medium which is merely carrying curvature
rigidity. This medium is at large distances indistinguishable from Einstein's
spacetime of general relativity. It does not support torsion and possesses
string-like curvature sources which in spacetime form world surfaces.Comment: 4 pages, submitted to Phys. Let. B: this is a polished version of
gr-qc/030703
Fokker-Planck and Langevin Equations from Forward--Backward Path Integral
Starting from a forward--backward path integral of a point particle in a bath
of harmonic oscillators, we derive the Fokker-Planck and Langevin equations
with and without inertia. Special emphasis is placed upon the correct operator
order in the time evolution operator. The crucial step is the evaluation of a
Jacobian with a retarded time derivative by analytic regularization.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/31
Efficient Algorithm for Perturbative Calculation of Multiloop Feynman Integrals
We present an efficient algorithm for calculating multiloop Feynman integrals
perturbatively.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals
In perturbative calculations of quantum-statistical zero-temperature path
integrals in curvilinear coordinates one encounters Feynman diagrams involving
multiple temporal integrals over products of distributions, which are
mathematically undefined. In addition, there are terms proportional to powers
of Dirac delta-functions at the origin coming from the measure of path
integration. We give simple rules for integrating products of distributions in
such a way that the results ensure coordinate independence of the path
integrals. The rules are derived by using equations of motion and partial
integration, while keeping track of certain minimal features originating in the
unique definition of all singular integrals in dimensions. Our
rules yield the same results as the much more cumbersome calculations in 1-
epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also
agree with the rules found in an independent treatment on a finite time
interval.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
Universality Principle for Orbital Angular Momentum and Spin in Gravity with Torsion
We argue that compatibility with elementary particle physics requires
gravitational theories with torsion to be unable to distinguish between orbital
angular momentum and spin. An important consequence of this principle is that
spinless particles must move along autoparallel trajectories, not along
geodesics.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re27
Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift
We develop a recursive method for perturbative solutions of the Fokker-Planck
equation with nonlinear drift. The series expansion of the time-dependent
probability density in terms of powers of the coupling constant is obtained by
solving a set of first-order linear ordinary differential equations. Resumming
the series in the spirit of variational perturbation theory we are able to
determine the probability density for all values of the coupling constant.
Comparison with numerical results shows exponential convergence with increasing
order.Comment: Author Information under
http://www.theo-phys.uni-essen.de/tp/ags/pelster_dir
Two-Loop Effective Potential of O(N)-Symmetric Scalar QED in 4-epsilon Dimensions
The effective potential of scalar QED is computed analytically up to two
loops in the Landau gauge. The result is given in 4-epsilon dimensions using
minimal subtraction and epsilon-expansions. In three dimensions, our
calculation is intended to help throw light on unsolved problems of the
superconducting phase transition, where critical exponents and the position of
the tricritical point have not yet found a satisfactory explanation within the
renormalization group approach.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/32
Generating Functionals for Harmonic Expectation Values of Paths with Fixed End Points. Feynman Diagrams for Nonpolynomial Interactions
We introduce a general class of generating functionals for the calculation of
quantum-mechanical expectation values of arbitrary functionals of fluctuating
paths with fixed end points in configuration or momentum space. The generating
functionals are calculated explicitly for harmonic oscillators with
time-dependent frequency, and used to derive a smearing formulas for
correlation functions of polynomial and nonpolynomials functions of
time-dependent positions and momenta. These formulas summarize the effect of
thermal and quantum fluctuations, and serve to derive generalized Wick rules
and Feynman diagrams for perturbation expansions of nonpolynomial interactions.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/28
Solution of Coulomb Path Integral in Momentum Space
The path integral for a point particle in a Coulomb potential is solved in
momentum space. The solution permits us to give for the first time a negative
answer to an old question of quantum mechanics in curved spaces raised in 1957
by DeWitt, whether the Hamiltonian of a particle in a curved space contains an
additional term proportional to the curvature scalar . We show that this
would cause experimentally wrong level spacings in the hydrogen atom. Our
solution also gives a first experimental confirmation of the correctness of the
measure of integration in path integrals in curved space implied by a recently
discovered nonholonomic mapping principle.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re/27
Addendum to paper: Strong-Coupling Behavior of -Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
The graphical extrapolation procedure to infinite order of variational
perturbation theory in a recent calculation of critical exponents of
three-dimensional -theories at infinite couplings is improved by
another way of plotting the results.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re257a/preprint.htm
- …