Spectral Representation of the Covariant Two‐Point Function and Infinite‐Component Fields with Arbitrary Mass Spectrum

1969 ◽  
Vol 10 (11) ◽  
pp. 2014-2019 ◽  
Author(s):  
I. T. Todorov ◽  
R. P. Zaikov
Keyword(s):  
Mass Spectrum ◽  
Spectral Representation ◽  
Point Function ◽  
Arbitrary Mass ◽  
Infinite Component

scholarly journals Loops in AdS: from the spectral representation to position space. Part II

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dean Carmi
Keyword(s):  
Spectral Representation ◽  
Tree Level ◽  
Point Function ◽  
Position Space ◽  
Gross Neveu Model ◽  
Loop Amplitudes

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

scholarly journals FREE ENERGY DECREASES ALONG WILSON RENORMALIZATION GROUP TRAJECTORIES

1995 ◽  
Vol 10 (21) ◽  
pp. 1543-1548 ◽  
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Spectral Representation ◽  
Point Function ◽  
Cutoff Function ◽  
Wilson Renormalization Group

The free energy is shown to decrease along Wilson renormalization group trajectories, in a dimension-independent fashion, for d>2. The argument assumes the monotonicity of the cutoff function, and positivity of a spectral representation of the two-point function. The argument is valid for all orders in perturbation theory.

scholarly journals UNPARTICLE AS A PARTICLE WITH ARBITRARY MASS

2008 ◽  
Vol 23 (31) ◽  
pp. 2645-2649 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Mass Spectrum ◽  
Field Operator ◽  
Arbitrary Mass ◽  
Continuous Mass ◽  
Ordinary Particle

The unparticle field operator can be expanded in terms of creation and destruction operators corresponding to particles with a continuous mass spectrum. Hence, when the four-momentum of an unparticle is measured, then the unparticle manifests as an ordinary particle with a definite (but arbitrary) mass.

SCALAR FIELD THEORY IN THE AdS/CFT CORRESPONDENCE: AN OPERATOR FORMULATION

2007 ◽  
Vol 22 (30) ◽  
pp. 2287-2295 ◽  
Author(s):  
G. A. KERIMOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Fields ◽  
De Sitter Space ◽  
De Sitter ◽  
Point Function ◽  
Scalar Field Theory ◽  
Arbitrary Mass ◽  
Boundary Limit ◽  
Operator Formulation

Starting with a scalar field theory in Euclidean anti-de Sitter space constructed in an earlier paper, we examine the boundary limit of the quantized bulk field. Our AdS/CFT correspondence is generally valid for interacting fields, and is illustrated by a treatment of three-point function for scalar fields of arbitrary mass.

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