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Excited states of bosons and fermions in a four-Fermi quantum field theory
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Excited States of Bosons and Fermions in a Four-Fermi
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Quantum Field Theory. P.
FURLAN.
International School for Advanced Studies (SISSA), Trieste, Italy, Istituto di Fisica Teorica dell’Universita’ di Trieste, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy: AND R. R~CZKA. International School for Advanced Studies (SISSA), Trieste. Italy and Institute of Nuclear Research, Warsaw, Poland. A scalar-pseudoscalar four-Fermi quantum field model in four-dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons the path-integral representation for the generating functional for Green’s functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classical ground-state solution for collective bosom a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectories for bosons are approximately linear in J. as the experimental trajectories. The existence of fermion bound or excited states depend on the value of the dynamical parameters of the model. For some values of dynamical parameters there are bound states for J = 4 and :. However. for most of other values bound or excited fermion states do not exist.
Quantum Tunnelling in u Dissipative System. A. 0. CALDEIRA. Universidade Estadual de Campinas. Paolo, Brazil; AND A. J. LEGGET. Sussex, Falmer. Brighton BNI 9QH,
Cidade Universitaria, School of Mathematical England.
Instituto de Fisica “Gleb Waraghin.” Barao Geraldo, 13-100 Campinas Sao and Physical Sciences, University of
The question “what is the effect of dissipation of quantum tunnelling?” is motivated, defined and resolved. The question is of particular interest in the context of tunnelling of a macroscopic variable such as the trapped flux in a SQUID, where it is shown that it is crucial to resolve it in the context of tests of the validity of quantum mechanics at the macroscopic level. but it is also relevant to various microscopic tunnelling situations. The question is defined as follows: Suppose there exists a system. which has a metastable minimum and whose quasiclassical equation of motion in the region near the minimum is given by
Mj’ + 114+ W/aq = F,,,(t), where the potential V(q) and friction coefftcient n are regarded as experimentally determined quantities (and the energy dissipated irreversibly per unit time is simply ~4’). How does the tunnelling behaviour of such a system at T = 0 differ from that of one obeying a similar equation, with the same potential V(q) and mass M, but with friction coefficient r] equal to zero?
Primed
in Belgium
OF
PAPERS
TO
APPEAR
IN
Excited States of Bosons and Fermions in a Four-Fermi
FUTURE
235
ISSUES
Quantum Field Theory. P.
FURLAN.
International School for Advanced Studies (SISSA), Trieste, Italy, Istituto di Fisica Teorica dell’Universita’ di Trieste, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy: AND R. R~CZKA. International School for Advanced Studies (SISSA), Trieste. Italy and Institute of Nuclear Research, Warsaw, Poland. A scalar-pseudoscalar four-Fermi quantum field model in four-dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons the path-integral representation for the generating functional for Green’s functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classical ground-state solution for collective bosom a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectories for bosons are approximately linear in J. as the experimental trajectories. The existence of fermion bound or excited states depend on the value of the dynamical parameters of the model. For some values of dynamical parameters there are bound states for J = 4 and :. However. for most of other values bound or excited fermion states do not exist.
Quantum Tunnelling in u Dissipative System. A. 0. CALDEIRA. Universidade Estadual de Campinas. Paolo, Brazil; AND A. J. LEGGET. Sussex, Falmer. Brighton BNI 9QH,
Cidade Universitaria, School of Mathematical England.
Instituto de Fisica “Gleb Waraghin.” Barao Geraldo, 13-100 Campinas Sao and Physical Sciences, University of
The question “what is the effect of dissipation of quantum tunnelling?” is motivated, defined and resolved. The question is of particular interest in the context of tunnelling of a macroscopic variable such as the trapped flux in a SQUID, where it is shown that it is crucial to resolve it in the context of tests of the validity of quantum mechanics at the macroscopic level. but it is also relevant to various microscopic tunnelling situations. The question is defined as follows: Suppose there exists a system. which has a metastable minimum and whose quasiclassical equation of motion in the region near the minimum is given by
Mj’ + 114+ W/aq = F,,,(t), where the potential V(q) and friction coefftcient n are regarded as experimentally determined quantities (and the energy dissipated irreversibly per unit time is simply ~4’). How does the tunnelling behaviour of such a system at T = 0 differ from that of one obeying a similar equation, with the same potential V(q) and mass M, but with friction coefficient r] equal to zero?
Primed
in Belgium