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SUMMARY:AG Mathematische Physik\, Arnold Neumaier (Wien): Coherent Qua
 ntization II: Causal groups and quantum fields
UID:41da02ba-b37c-41b9-aa6a-230a4a118ed6
DESCRIPTION:Arnold Neumaier (Wien) Coherent Quantization II: Causal gr
 oups and quantum fields Abstract: This is the second of three lectures
  on coherent quantization and field theory to be given 11.-18.12.2023 
 in Erlangen (Germany). Causal groups are a new class of mathematical o
 bjects abstracted from the concept of dynamical C^*-algebras for quant
 um field theories introduced by Buchholz and Fredenhagen in their pape
 r Comm. Math. Phys. 377 (2020)\, 947-969. Unlike these authors (who ob
 tain their dynamical C^*-algebras from an analysis of causal perturbat
 iion theory) we motivate causal groups in a fully nonperturbative way 
 from the consideration of classical discrete-time dynamical systems. T
 his gives an intuitive understanding of the properties later assumed a
 xiomatically for causal groups over causal spaces (generalizing Minkow
 ski spacetime). Each causal group over Minkowski space gives rise to a
  particular dynamical C^*-algebra. The dynamical C^*-algebras of Buchh
 olz and Fredenhagen arise from abstract causal groups defined by gener
 ators and relations. We show how to construct causal groups over causa
 l spaces having a Tomonaga-Schwinger structure associated with an appr
 opriate classical many-fingered time dynamics. This gives a clear geom
 etric meaning to the new concept. Their unitary representations give n
 onperturbative constructions of nonrelativistic and relativistic quant
 um field theories. Conditions are given under which the Haag-Kastler a
 xioms or the Wightman axioms can be established. This reduces the rigo
 rous construction of realistic quantum field theories such as QED or Q
 CD to the (still unsettled) construction of unitary representations of
  causal groups with the properties defining QED or QCD. A constructed 
 QFT can be identified with a particular perturbatively defined one (su
 ch as QED or QCD) by performing aposteriori causal perturbation theory
  to lowest (1 loop) order. This lecture is essentially independent of 
 the first lecture. The slides of the lecture will pr
DTSTART:20231214T151500Z
DTEND:20231214T170000Z
LOCATION:Übung 1 / 01.250-128\, Erlangen
DTSTAMP:20260918T043958Z
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