LOCAL OPERATORS ON BANACH MODULES

2004 ◽  
Vol 104A (2) ◽  
pp. 239-248
Author(s):  
J. Bračič
Keyword(s):  
Banach Modules ◽  
Local Operators

scholarly journals Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. Liam Fitzpatrick ◽  
Emanuel Katz ◽  
Matthew T. Walters ◽  
Yuan Xin
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Fine Tuning ◽  
Yukawa Model ◽  
Spectral Functions ◽  
Scalar Superfield ◽  
Local Operators ◽  
Dimensionless Coupling ◽  
Zumino Model ◽  
Yukawa Theory

Abstract We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ2-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $$ \overline{g} $$ g ¯ , and is expected to have a critical point at a tuned value $$ {\overline{g}}_{\ast } $$ g ¯ ∗ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $$ \overline{g} $$ g ¯ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

scholarly journals Locality and entanglement of indistinguishable particles

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Till Jonas Frederick Johann ◽  
Ugo Marzolino
Keyword(s):  
Quantum Mechanics ◽  
Quantum Correlation ◽  
Indistinguishable Particle ◽  
Local Operators

AbstractEntanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies. While entanglement theory is well settled for distinguishable particles, there are five inequivalent approaches to entanglement of indistinguishable particles. We analyse the different definitions of indistinguishable particle entanglement in the light of the locality notion. This notion is specified by two steps: (i) the identification of subsystems by means of their local operators; (ii) the requirement that entanglement represent correlations between the above subsets of operators. We prove that three of the aforementioned five entanglement definitions are incompatible with any locality notion defined as above.

scholarly journals Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Guanda Lin ◽  
Gang Yang
Keyword(s):  
Form Factors ◽  
General Strategy ◽  
Dual Representation ◽  
Remainder Function ◽  
Full Color ◽  
Minimal Form ◽  
Planar Part ◽  
Dilatation Operator ◽  
Dependent Form ◽  
Local Operators

Abstract Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

scholarly journals Boundary dual of bulk local operators

2017 ◽  
Vol 96 (2) ◽  
Author(s):  
Fabio Sanches ◽  
Sean J. Weinberg
Keyword(s):  
Local Operators

scholarly journals Conformally invariant non-local operators

2001 ◽  
Vol 201 (1) ◽  
pp. 19-60 ◽  
Author(s):  
Thomas Branson ◽  
A. Rod Gover
Keyword(s):  
Conformally Invariant ◽  
Local Operators ◽  
Non Local

scholarly journals Design and Commissioning of a Community Scale Solar Powered Membrane-Based Water Purification System in Haiti

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Shavin Pinto ◽  
Yung Wong ◽  
Kyle Fennesy ◽  
Yan Tang ◽  
Mark Compare
Keyword(s):  
Water Purification ◽  
Ultrafiltration Membrane ◽  
Operator Training ◽  
Water Purification System ◽  
Filtration System ◽  
Purification System ◽  
Local Operators ◽  
Solar Powered ◽  
Proper Operation ◽  
Important Design

This paper presents the design and commissioning of a solar powered water purification system at the Ryan Epps Home for Children (REHC) in Michaud, Haiti. This systemsupplies clean drinking water to the 200 children who live and go to school at REHC and also tothe community in the form of a micro-business. This micro-business is the mechanism for incomegeneration for sustainable system operation. The purifier uses a three stage filtration system witha disc-type sediment filter, a 0.1 micron ultrafiltration membrane, and an ultraviolet light fordisinfection. The backwash cycle extends the life of the ultrafiltration membrane to 4 – 7 yearsbefore a new filter is required. Simplicity in operation was an important design considerationbecause it facilitates local operator training, and understanding. To further ensure completeunderstanding of operation, a pictorial quick-start manual was developed so that operators onlyneed to follow the diagrams laid out on the manual. The design folder with CAD drawings,schematics, datasheets, and troubleshooting guide are left with the local operators. Testingbefore shipping and after installation to ensure proper operation upon installation and on-sitewater quality testing ensures it will promote improved community health.

scholarly journals Rigorous bounds on dynamical response functions and time-translation symmetry breaking

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Marko Medenjak ◽  
Tomaz Prosen ◽  
Lenart Zadnik
Keyword(s):  
Dynamical Response ◽  
Response Functions ◽  
Xxz Model ◽  
Dynamical Symmetries ◽  
Time Translation ◽  
Spatially Inhomogeneous ◽  
Translation Symmetry ◽  
Local Operators ◽  
Rigorous Bounds ◽  
Translation Symmetry Breaking

Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

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