279 research outputs found
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
High-Order Variational Calculation for the Frequency of Time-Periodic Solutions
We develop a convergent variational perturbation theory for the frequency of
time-periodic solutions of nonlinear dynamical systems. The power of the theory
is illustrated by applying it to the Duffing oscillator.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster/,
http://www.physik.fu-berlin.de/~kleinert/ and
http://www.informatik.uni-stuttgart.de/ipvr/bv/personen/schanz.htm
Functional Closure of Schwinger-Dyson Equations in Quantum Electrodynamics, Part 1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
Using functional derivatives with respect to free propagators and
interactions we derive a closed set of Schwinger-Dyson equations in quantum
electrodynamics. Its conversion to graphical recursion relations allows us to
systematically generate all connected and one-particle irreducible Feynman
diagrams for the -point functions and the vacuum energy together with their
correct weights.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/32
Quantum Statistics of Hydrogen in Strong Magnetic Fields
By an extension of the Feynman-Kleinert variational approach, we calculate
the temperature-dependent effective classical potential governing the quantum
statistical properties of a hydrogen atom in a uniform magnetic field. In the
zero-temperature limit, we obtain ground state energies which are accurate for
all magnetic field strengths from weak to strong fields.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/30
The asymmetric energy of single-closed-shell nuclei in present-day microscopic theory
M.S.R. Martin Ahren
Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics
We present a method for a recursive graphical construction of Feynman
diagrams with their correct multiplicities in quantum electrodynamics. The
method is first applied to find all diagrams contributing to the vacuum energy
from which all n-point functions are derived by functional differentiation with
respect to electron and photon propagators, and to the interaction. Basis for
our construction is a functional differential equation obeyed by the vacuum
energy when considered as a functional of the free propagators and the
interaction. Our method does not employ external sources in contrast to
traditional approaches.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
Critical Exponents of the Superconducting Phase Transition
We study the critical exponents of the superconducting phase transition in
the context of renormalization group theory starting from a dual formulation of
the Ginzburg-Landau theory. The dual formulation describes a loop gas of
Abrikosov flux tubes which proliferate when the critical temperature is
approached from below. In contrast to the Ginzburg-Landau theory, it has a
spontaneously broken global symmetry and possesses an infrared stable fixed
point. The exponents coincide with those of a superfluid with reversed
temperature axis.Comment: Postscript file. For related work see www adress
http://www.physik.fu-berlin.de/kleiner_re.html in our homepage
http://www.physik.fu-berlin.de/kleinert.htm
Non-abelian descendant of abelian duality in a two-dimensional frustrated quantum magnet
Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson
paradigm have led to a number of field theories, potentially important for
certain two-dimensional magnetic insulating systems, where criticality is not
very well understood. This situation highlights the need for non-perturbative
information about criticality in two spatial dimensions (three space-time
dimensions), which is a longstanding challenge. As a step toward addressing
these issues, we present evidence that the O(4) vector model is dual to a
theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both
field theories arise as low-energy, long-wavelength descriptions of a
frustrated XY model on the triangular lattice. Abelian boson-vortex duality of
the lattice model, together with the emergence of larger non-abelian symmetry
at low energies, leads to this rare example of duality in two spatial
dimensions involving non-abelian global symmetry and fermions, but without
supersymmetry. The duality can also be viewed as a bosonization of the Dirac
fermion gauge theory.Comment: 12 pages + 3 appendices. 3 figures. Minor change, typos correcte
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