NDLI: On Energy-Momentum Transfer of Quantum Fields

Content Provider	Springer Nature Link
Author	Herdegen, Andrzej
Copyright Year	2014
Abstract	We prove the following theorem on bounded operators in quantum field theory: if $${\\|[B,B^*(x)]\\|\leqslant{\rm const}D(x)}$$ , then $${\\|B^k_\pm(\nu)G(P^0)\\|^2\leqslant{\rm const}\int D(x - y){\rm d}\|\nu\|(x){\rm d}\|\nu\|(y)}$$ , where D(x) is a function weakly decaying in spacelike directions, $${B^k_\pm}$$ are creation/annihilation parts of an appropriate time derivative of B, G is any positive, bounded, non-increasing function in $${L^2(\mathbb{R})}$$ , and $${\nu}$$ is any finite complex Borel measure; creation/annihilation operators may be also replaced by $${B^k_t}$$ with $${\check{B^k_t}(p)=\|p\|^k\check{B}(p)}$$ . We also use the notion of energy-momentum scaling degree of B with respect to a submanifold (Steinmann-type, but in momentum space, and applied to the norm of an operator). These two tools are applied to the analysis of singularities of $${\check{B}(p)G(P^0)}$$ . We prove, among others, the following statement (modulo some more specific assumptions): outside p = 0 the only allowed contributions to this functional which are concentrated on a submanifold (including the trivial one—a single point) are Dirac measures on hypersurfaces (if the decay of D is not to slow).
Ending Page	1280
Page Count	18
Starting Page	1263
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	10
Volume Number	104
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-06-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry translation automorphism group Theoretical, Mathematical and Computational Physics quantum field theory spectral properties Group Theory and Generalizations Axiomatic quantum field theory; operator algebras Statistical Physics, Dynamical Systems and Complexity Automorphisms
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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