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On loop space formulation of gauge theories
254
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not integrable, their probability distributions do have a recognizable pattern which moves classically. Such states form a complete set only if generated from energy eigenstates with definite parity. If generated from scattering eigenstates, only certain special coherent states are physically admissible, and these do not form a complete set. The elTects of resistive (energy dissipating) forces and of thermal agitation are considered briefly. At zero temperature ordinary resistive mechanisms enhance the sojourn time.
Numerical Simulations of Department, University Scotland.
Two-Dimensional of Edinburgh,
QED. S. R. CARSON AND R. D. KENWAY. The King’s Buildings, Maytield Road, Edinburgh
Physics EH9 352,
We describe the computer simulation of 2-dimensional QED on a 64 x 64 Euclidean spacetime lattice using the Susskind lattice fermion action. The order parameter for chiral symmetry breaking and the low-lying meson masses are calculated for both the model with two continuum flavours, which arises naturally in this formulation, and the model with one continuum flavour obtained by including a nonsymmetric mass term and setting one fermion mass equal to the cut-off. Results are compared with those obtained using the quenched approximation, and with analytic predictions.
Canonical Pafh Integral Quantization of Gauge Systems. Crete, Iraklion, Greece and CERN, Geneva.
P. DITSAS. Physics
Department,
University
of
It is shown that the (possibly explicity time-dependent) gauge fixing conditions zO(q. p, t) = 0, invoked for the canonical quantization of gauge theories via the Faddeev path integral formulation, need not satisfy the restrictions { zo. 2,) = 0. As a preparation, we re-examine and clarify how the canonical structure on the large (partly unphysical) phaseespace induces, through either Poisson brackets or Lagrange brackets or Dirac brackets, the canonical structure on the physical space of observables. The realizability of some particularly convenient coordinate systems on r is also proved.
A Practical Guide to the Next-to-Leading Order of lhe Perturbation Expansion. M. PRASZALOWICZ, Institute of Physics, Jagellonian University, Cracow, Poland; Max Planck-Institut fiir Physick und Astrophysik, Werner Heisenberg-Institute Munich 40, Federal Republic of Germany.
A. NOWAK AND M. AND W. SLOMINSKI, fiir Physik, D-8000
The formulae useful for the calculation of the partonic cross sections in the next-to-leading order of pcrturbative expansion in massless QCD are given. In particular the renormalized vertex functions and propagators, the rules for the evaluating of “box” diagrams, and integrals over 2- and 3-particle phasespace are presented. Ultraviolet and infrared divergencies are dimensionally regularized and the MS renormalization scheme is adopted.
On Loop Space Formulation of Gauge Theories. HONG-MO Appleton Laboratory Chilton, Didcot, Oxon OX11 Mathematical Institute, 24-29 St. Giles, Oxford, OXI
CHAN AND PETER SCHARBACH, Rutherford OQX, England; AND SHEUNG TSUN TSOU, 3LB, England.
In attempting to formulate gauge theories entirely in terms of loop variables, it is found convenient to work in the function space of parametrised loops with the loop space connection FJCjs) as tield variables. Equivalence to the conventional formulation in terms of the gauge potential A,(x) is ensured by imposing on F,(Cls) certain conditions implying the local absence of “magnetic sources” or monopoles. These conditions are reminiscent of the Poincart: lemma in electromagnetism, and establish a
ABSTRACTS
OF PAPERS
TO APPEAR
IN FUTURE
255
ISSUES
one-one correspondence between F,(Cls) so constrained and A,(x) up to gauge equivalence. We use this approach to reformulate the action principle for pure gauge theories and to derive field equations from it completely in terms of loop variables. We believe that the formalism is useful in the theory of monopoles and may also find application in lattice calculations.
Analytic Solutions of Friedman Equation for Spatially Opened Universes with Cosmological Constant and Radiation Pressure. M. D@ROWSKI, Astronomical Observatory of the Wroclaw University, University of Wroclaw, ul. Kopernika 11, 51-622 Wroclaw, Poland; AND J. STELMACH, Institute of Theoretical Physics, University of Wroclaw, ul. Cybulskiego 36, SO-205 Wrodaw. Poland. Present paper is a continuation of a discussion given by R. Coquereaux and A. Grossmann on analytic solutions of spatially closed Friedman universes with cosmological constant and radiation pressure. Our purpose is to find such solutions in the case of opened universes, Explicit formulae are given.
Primed
in Belgium
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
not integrable, their probability distributions do have a recognizable pattern which moves classically. Such states form a complete set only if generated from energy eigenstates with definite parity. If generated from scattering eigenstates, only certain special coherent states are physically admissible, and these do not form a complete set. The elTects of resistive (energy dissipating) forces and of thermal agitation are considered briefly. At zero temperature ordinary resistive mechanisms enhance the sojourn time.
Numerical Simulations of Department, University Scotland.
Two-Dimensional of Edinburgh,
QED. S. R. CARSON AND R. D. KENWAY. The King’s Buildings, Maytield Road, Edinburgh
Physics EH9 352,
We describe the computer simulation of 2-dimensional QED on a 64 x 64 Euclidean spacetime lattice using the Susskind lattice fermion action. The order parameter for chiral symmetry breaking and the low-lying meson masses are calculated for both the model with two continuum flavours, which arises naturally in this formulation, and the model with one continuum flavour obtained by including a nonsymmetric mass term and setting one fermion mass equal to the cut-off. Results are compared with those obtained using the quenched approximation, and with analytic predictions.
Canonical Pafh Integral Quantization of Gauge Systems. Crete, Iraklion, Greece and CERN, Geneva.
P. DITSAS. Physics
Department,
University
of
It is shown that the (possibly explicity time-dependent) gauge fixing conditions zO(q. p, t) = 0, invoked for the canonical quantization of gauge theories via the Faddeev path integral formulation, need not satisfy the restrictions { zo. 2,) = 0. As a preparation, we re-examine and clarify how the canonical structure on the large (partly unphysical) phaseespace induces, through either Poisson brackets or Lagrange brackets or Dirac brackets, the canonical structure on the physical space of observables. The realizability of some particularly convenient coordinate systems on r is also proved.
A Practical Guide to the Next-to-Leading Order of lhe Perturbation Expansion. M. PRASZALOWICZ, Institute of Physics, Jagellonian University, Cracow, Poland; Max Planck-Institut fiir Physick und Astrophysik, Werner Heisenberg-Institute Munich 40, Federal Republic of Germany.
A. NOWAK AND M. AND W. SLOMINSKI, fiir Physik, D-8000
The formulae useful for the calculation of the partonic cross sections in the next-to-leading order of pcrturbative expansion in massless QCD are given. In particular the renormalized vertex functions and propagators, the rules for the evaluating of “box” diagrams, and integrals over 2- and 3-particle phasespace are presented. Ultraviolet and infrared divergencies are dimensionally regularized and the MS renormalization scheme is adopted.
On Loop Space Formulation of Gauge Theories. HONG-MO Appleton Laboratory Chilton, Didcot, Oxon OX11 Mathematical Institute, 24-29 St. Giles, Oxford, OXI
CHAN AND PETER SCHARBACH, Rutherford OQX, England; AND SHEUNG TSUN TSOU, 3LB, England.
In attempting to formulate gauge theories entirely in terms of loop variables, it is found convenient to work in the function space of parametrised loops with the loop space connection FJCjs) as tield variables. Equivalence to the conventional formulation in terms of the gauge potential A,(x) is ensured by imposing on F,(Cls) certain conditions implying the local absence of “magnetic sources” or monopoles. These conditions are reminiscent of the Poincart: lemma in electromagnetism, and establish a
ABSTRACTS
OF PAPERS
TO APPEAR
IN FUTURE
255
ISSUES
one-one correspondence between F,(Cls) so constrained and A,(x) up to gauge equivalence. We use this approach to reformulate the action principle for pure gauge theories and to derive field equations from it completely in terms of loop variables. We believe that the formalism is useful in the theory of monopoles and may also find application in lattice calculations.
Analytic Solutions of Friedman Equation for Spatially Opened Universes with Cosmological Constant and Radiation Pressure. M. D@ROWSKI, Astronomical Observatory of the Wroclaw University, University of Wroclaw, ul. Kopernika 11, 51-622 Wroclaw, Poland; AND J. STELMACH, Institute of Theoretical Physics, University of Wroclaw, ul. Cybulskiego 36, SO-205 Wrodaw. Poland. Present paper is a continuation of a discussion given by R. Coquereaux and A. Grossmann on analytic solutions of spatially closed Friedman universes with cosmological constant and radiation pressure. Our purpose is to find such solutions in the case of opened universes, Explicit formulae are given.
Primed
in Belgium