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On the regularization of a class of divergent Feynman integrals in covariant and axial gauges
ABSTRACTS On
the
of
Regularization
a Class
OF PAPERS
of
Divergent
HOONG-CHIEN LEE .AND MICHAEL Nuclear Laboratories. Chalk River.
TO APPEAR Feynman
IN FUTURE Integrals
S. MILGRAM. Atomic Energy Ontario. Canada KOJ IJO.
in
305
ISSUES Couariant
of Canada
and
Axial
Limited.
Gauges.
Chalk
River
A hybrid of dimensional and analytic regularization is used to regulate and uncover a Meijer’s Gfunction representation for a class of massless, divergent Feynman integrals in an axial gauge. Integrals in the covariant gauge belong to a subclass and those in the light-cone gauge are reached by analytic continuation. The method decouples the physical ultraviolet and infrared singularities from the spurious axial gauge singularity but regulates all three simultaneously. For the axial gauge singularity, the new analytic method is more powerful and elegant than the old principal value prescription. but the two methods yield identical infinite as well as regular parts.
The
Obserr~ation
York
YOI
of Deca!.. A. SUDBERY. 5DD. United Kingdom.
Department
of Mathematics.
University
of York.
Heslington.
It is argued that the usual formulation of quantum mechanics does not satisfactorily describe physical change: the standard formula for a transition probability does not follow from the postulates. Instead. these yield the paradox that a watched pot never boils (sometimes called “Zeno‘s paradox”). The paradox is reviewed and the possibility of avoiding tt is discussed. A simple model of a decaying system is analysed; the system is then considered in continuous interaction with an apparatus designed to observe the time development of the system. In the light of this analysis. the possibility of replacing the usual (discrete) projection postulate by a continuous projection postulate is considered.
Scaling
Lab>* in the
Department
Ordering
of Physics.
Process
Kyushu
of Quenched
University.
Thermodynamicall~~
Fukuoka
Unstable
Systems.
TAKAO
OHTA.
8 12. Japan.
Dynamics of phase separation in quenched thermodynamically unstable systems is studied. The scaling law exhibited in the late stage of the ordering process is investigated by the interface model. In the kinetics of the order-disorder transition the motion of random interfaces is shown to be responsible to the scaling law. The scaling form of the scattering function is obtained with particular attention to the fluctuating thermal noises. A droplet picture is used to discuss spinodal decomposition of off-critically quenched binary fluids. The scaling function is calculated explicitly in the region where the Brownian coagulation is most dominant for the phase separation. It is shown that the thermal noises are relevant to the scaling law in the ordering process driven by the Brownian coagulation whereas they are negligible in the kinetics of order-disorder transition.
the
of
Regularization
a Class
OF PAPERS
of
Divergent
HOONG-CHIEN LEE .AND MICHAEL Nuclear Laboratories. Chalk River.
TO APPEAR Feynman
IN FUTURE Integrals
S. MILGRAM. Atomic Energy Ontario. Canada KOJ IJO.
in
305
ISSUES Couariant
of Canada
and
Axial
Limited.
Gauges.
Chalk
River
A hybrid of dimensional and analytic regularization is used to regulate and uncover a Meijer’s Gfunction representation for a class of massless, divergent Feynman integrals in an axial gauge. Integrals in the covariant gauge belong to a subclass and those in the light-cone gauge are reached by analytic continuation. The method decouples the physical ultraviolet and infrared singularities from the spurious axial gauge singularity but regulates all three simultaneously. For the axial gauge singularity, the new analytic method is more powerful and elegant than the old principal value prescription. but the two methods yield identical infinite as well as regular parts.
The
Obserr~ation
York
YOI
of Deca!.. A. SUDBERY. 5DD. United Kingdom.
Department
of Mathematics.
University
of York.
Heslington.
It is argued that the usual formulation of quantum mechanics does not satisfactorily describe physical change: the standard formula for a transition probability does not follow from the postulates. Instead. these yield the paradox that a watched pot never boils (sometimes called “Zeno‘s paradox”). The paradox is reviewed and the possibility of avoiding tt is discussed. A simple model of a decaying system is analysed; the system is then considered in continuous interaction with an apparatus designed to observe the time development of the system. In the light of this analysis. the possibility of replacing the usual (discrete) projection postulate by a continuous projection postulate is considered.
Scaling
Lab>* in the
Department
Ordering
of Physics.
Process
Kyushu
of Quenched
University.
Thermodynamicall~~
Fukuoka
Unstable
Systems.
TAKAO
OHTA.
8 12. Japan.
Dynamics of phase separation in quenched thermodynamically unstable systems is studied. The scaling law exhibited in the late stage of the ordering process is investigated by the interface model. In the kinetics of the order-disorder transition the motion of random interfaces is shown to be responsible to the scaling law. The scaling form of the scattering function is obtained with particular attention to the fluctuating thermal noises. A droplet picture is used to discuss spinodal decomposition of off-critically quenched binary fluids. The scaling function is calculated explicitly in the region where the Brownian coagulation is most dominant for the phase separation. It is shown that the thermal noises are relevant to the scaling law in the ordering process driven by the Brownian coagulation whereas they are negligible in the kinetics of order-disorder transition.