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Factorization Algebras in Quantum Field Theory: Volume 2
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.
Renormalization and Effective Field Theory
Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
String-Math 2022
This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
Factorization Algebras in Quantum Field Theory
This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
The Photograph
A 20-year-old photograph picturing six young men is sent to Michael Adams, a private detective in Chicago. Michael then receives a phone call from one of the faces in the picture. It seems another man in the group photo has apparently just taken his own life. The detective decides to fly home to New York and attend the funeral, where he can meet up with the caller, Ritchie Sweet. Ritchie suspects his friend's suicide was really foul play, but can't prove it. Michael is stymied, until Ritchie is killed trying to pass the detective a clue to prove that the suicide was really murder. Michael then realizes that each person in The Photograph is in jeopardy, so he races to find the remaining men a...
The Admiralty Sessions, 1536-1834
The growth in England and Britain’s merchant marine from the medieval period onwards meant that an increasing number of criminal offences were committed on or against the country’s vessels while they were at sea. Between 1536 and 1834, such crimes were determined at the Admiralty Sessions if brought to trial. This was a special part of the wider Admiralty Court, which, unlike the other forums in that tribunal, used English common law procedure rather than Roman civil law to try its cases. To a modest extent, this produced a ‘hybrid’ court, dominated by the common law but influenced by aspects of Europe’s other major legal tradition. The Admiralty Sessions also had their own (highly...
The Law of Habeas Corpus in Ireland
Habeas corpus - the common law process for obtaining the release of the illegally detained - is now embedded in the Irish legal system as Article 40.4.2 of the Constitution of Ireland. The law of habeas corpus in Ireland is the first full study of Article 40.4.2. It provides an account of the historical development of the remedy in Ireland, of the character of the investigation conducted on an Article 40.4.2 enquiry, and of the procedural features of the remedy.
Marriage in Ireland, 1660–1925
Explores how marriage in Ireland was perceived, negotiated and controlled by church and state as well as by individuals across three centuries.
