The Octagon Form Factor in $$\mathcal {N}=4$$ SYM and Free Fermions

2020 ◽  
pp. 113-134
Author(s):  
Ivan Kostov
Keyword(s):  
Form Factor ◽  
Free Fermions

scholarly journals Octagon with finite bridge: free fermions and determinant identities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Ivan Kostov ◽  
Valentina B. Petkova
Keyword(s):  
Form Factor ◽  
Correlation Functions ◽  
Fock Space ◽  
Similarity Transformation ◽  
Operator Representation ◽  
Free Fermions ◽  
Expectation Value ◽  
Point Correlation ◽  
Dirac Sea ◽  
Kinematical Parameters

Abstract We continue the study of the octagon form factor which helps to evaluate a class of four-point correlation functions in $$ \mathcal{N} $$ N = 4 SYM theory. The octagon is characterised, besides the kinematical parameters, by a “bridge” of ℓ propagators connecting two nonadjacent operators. In this paper we construct an operator representation of the octagon with finite bridge as an expectation value in the Fock space of free complex fermions. The bridge ℓ appears as the level of filling of the Dirac sea. We obtain determinant identities relating octagons with different bridges, which we derive from the expression of the octagon in terms of discrete fermionic oscillators. The derivation is based on the existence of a previously conjectured similarity transformation, which we find here explicitly.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

MAGNETIC FORM FACTOR MEASUREMENTS IN CERIUM HEXABORIDE

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-273-C7-278 ◽  
Author(s):  
P. Burlet ◽  
J. X. Boucherle ◽  
J. Rossat-Mignod ◽  
J. W. Cable ◽  
W. C. Koehler ◽  
...  
Keyword(s):  
Form Factor ◽  
Magnetic Form Factor

FORM FACTOR MEASUREMENTS IN CeTe

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-263-C7-271 ◽  
Author(s):  
J. X. Boucherle ◽  
D. Ravot ◽  
J. Schweizer
Keyword(s):  
Form Factor

FORM FACTOR MEASUREMENT IN FERROMAGNETIC COBALT ORTHOVANADATE

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-253-C7-256
Author(s):  
H. Fuess ◽  
R. Müller ◽  
D. Schwabe ◽  
F. Tasset
Keyword(s):  
Form Factor ◽  
Factor Measurement ◽  
Ferromagnetic Cobalt

Super-Conducting Quantum Interference Device Technique: 3-D Localization of a Short within a Flip Chip Assembly

2001 ◽  
Author(s):  
Kendall Scott Wills ◽  
Omar Diaz de Leon ◽  
Kartik Ramanujachar ◽  
Charles P. Todd
Keyword(s):  
Form Factor ◽  
Failure Analysis ◽  
Time Domain ◽  
Quantum Interference ◽  
Flip Chip ◽  
Time Domain Reflectometry ◽  
Interfacial Region ◽  
Precise Localization ◽  
Super Conducting ◽  
Accuracy Of Measurement

Abstract In the current generations of devices the die and its package are closely integrated to achieve desired performance and form factor. As a result, localization of continuity failures to either the die or the package is a challenging step in failure analysis of such devices. Time Domain Reflectometry [1] (TDR) is used to localize continuity failures. However the accuracy of measurement with TDR is inadequate for effective localization of the failsite. Additionally, this technique does not provide direct 3-Dimenstional information about the location of the defect. Super-conducting Quantum Interference Device (SQUID) Microscope is useful in localizing shorts in packages [2]. SQUID microscope can localize defects to within 5um in the X and Y directions and 35um in the Z direction. This accuracy is valuable in precise localization of the failsite within the die, package or the interfacial region in flipchip assemblies.

Form Factor of an Open-Shell Atom

2000 ◽  
Vol 89 (1) ◽  
pp. 4
Author(s):  
A. N. Khoperskiı̆
Keyword(s):  
Form Factor ◽  
Open Shell

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

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