Il Nuovo Cimento A (1965-1970)

, Volume 66, Issue 3, pp 536–554 | Cite as

Quantum field theory on lightlike slabs

  • H. Leutwyler
  • J. R. Klauder
  • L. Streit


Restricting the support of relativistic quantum fields to lightlike hyperplanes (e.g. x0+x3)=const) we find examples of such fields to exist as well-defined self-adjoint operators with properties however that differ vastly from those of fields on the usual spacelike surfaces. We show that on a lightlike hyperplane 1) the free-field algebra is irreducible (instead of Abelian, and in contrast to what one would expect of data on a characteristic surface) and 2) fields with different masses become unitarily equivalent (whereas they are inequivalent on spacelike planes). Furthermore the field algebra restricted to the space-time slab between two parallel lightlike planes is always irreducible (while there are counterexamples for spacelike slabs). We establish this directly for generalized free fields and rederive it for Wightman fields in gereral.


Free Field Spacelike Surface Canonical Pair Weyl Operator Field Algebra 
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Квантовая теория поля в светоподобных плоскопараллельных слоях


Ограничиваясь подтверждением релятивистских квантовых полей на светоподобных гиперплоскостях (t.e.,x0+x3=const), мы находим, что примеры таких полей существуют, как отчетливо выраженные самосопряженные операторы со свойствами, которые, однако, существенно отличаются от свойств полей на обычных пространственноподобных поверхностях. Мы показываем, что на светоподобной гиперплоскости 1) алгебра свободного поля является неприводимой (вместо абелевой и, в противоположность тому, что следовало бы из данных на характеристической поверхности) и 2) поля с различными массами становятся унитарно эквивалентными (в то время как они являются неэквивалентными на пространст-венноподобных плоскостях). Кроме того, алгебра полей, ограниченная простран-ственноподобным плоскопараллеляным слоем между двумя светоподобными плоскостями, всегда является неприводимой (тогда как существуют контр-примеры для пространственноподобных плоскопараллельных слоев). Мы устанавливаем это непосредственно для обобщенных свободных полей и, в общем случае, заново выводим для полей Вайтмана.


Restringendo la base dei campi relativistici quantizzati agli iperpiani tipo luce (p.e.x0+x3=costante), si trovano esempi che confermano l'esistenza di tali campi come operatori autoaggiunti ben definiti ma con proprietà che differiscono molto da quelle dei campi sulle normali superfici spacelike. Si dimostra che su di un iperpiano tipo luce 1) l'algebra dei campi liberi è irriducibile (invece che abeliana, in contrasto con quanto ci si aspetterebbe dai dati su di una superficie caratteristica) e 2) campi con masse differenti divengono unitariamente equivalenti (mentre non lo sono su piani tipo spazio). Inoltre l'algebra dei campi ristretta alla lastra spaziotemporale fra due piani tipo luce paralleli è sempre irriducibile (mentre vi sono controesempi per le lastre tipo spazio). Si stabilisce ciò direttamente per campi liberi generalizzati e lo si ricava di nuovo per i campi di Wightman in generale.


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Copyright information

© Società Italiana di Fisica 1970

Authors and Affiliations

  • H. Leutwyler
    • 1
  • J. R. Klauder
    • 2
  • L. Streit
    • 2
  1. 1.CERNGenevaSwitzerland
  2. 2.Bell Telephone Laboratories, IncorporatedMurray HillUSA

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