scholarly journals Boundary operators associated with the Paneitz operator

2018 ◽  
Vol 67 (1) ◽  
pp. 293-327 ◽  
Author(s):  
Jeffrey Case
Keyword(s):  
Paneitz Operator ◽  
Boundary Operators

scholarly journals NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1430001 ◽  
Author(s):  
V. K. DOBREV
Keyword(s):  
Representation Theory ◽  
Theoretical Perspective ◽  
Explicit Construction ◽  
Intertwining Operators ◽  
Difference Operators ◽  
Semisimple Lie Groups ◽  
Boundary Operators ◽  
Boundary Fields ◽  
Theoretical Results ◽  
Schrödinger Algebra

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

scholarly journals Boundary contributions of on-shell recursion relations with multiple-line deformation

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Chang Hu ◽  
Xiao-Di Li ◽  
Yi Li
Keyword(s):  
Recursion Relation ◽  
Background Field ◽  
Field Method ◽  
Tree Level ◽  
Link Type ◽  
Multiple Line ◽  
Boundary Operators ◽  
Background Field Method ◽  
The Right ◽  
Boundary Behaviors

AbstractThe on-shell recursion relation has been recognized as a powerful tool for calculating tree-level amplitudes in quantum field theory, but it does not work well when the residue of the deformed amplitude $$\hat{A}(z)$$ A ^ ( z ) does not vanish at infinity of z. However, in such a situation, we still can get the right amplitude by computing the boundary contribution explicitly. In Arkani-Hamed and Kaplan (JHEP 04:076. 10.1088/1126-6708/2008/04/076. arXiv:0801.2385, 2008), the background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has been generalized to calculate the explicit boundary operators of some amplitudes with BCFW-like deformation in Jin and Feng (JHEP 04:123. 10.1007/JHEP04(2016)123. arXiv:1507.00463, 2016). In this paper, we will take a step further to generalize the method to the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method.

scholarly journals Boundary operators of BCFW recursion relation

2016 ◽  
Vol 2016 (4) ◽  
pp. 1-21 ◽  
Author(s):  
Qingjun Jin ◽  
Bo Feng
Keyword(s):  
Recursion Relation ◽  
Boundary Operators
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