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Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]
Nature CommunicationsVariational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Enrico Fontana +7 more
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Torus knots in adjoint representation and Vogel’s universality
European Physical Journal C: Particles and FieldsVogel’s universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $$\alpha ,\beta ,\gamma $$ α , β , γ , which are homogeneous coordinates of Vogel’s plane.
Liudmila Bishler, Andrei Mironov
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Lie Supergroups Obtained from 3-Dimensional Lie Superalgebras Associated to the Adjoint Representation and Having a 2-Dimensional Derived Ideal [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We give the explicit multiplication law of the Lie supergroups for which the base manifold is a 3-dimensional Lie group and whose underlying Lie superalgebra g=g0⊕g1 which satisfies g1=g0, g0 acts on g1 via the adjoint representation and g0 has a 2 ...
I. Hernández, R. Peniche
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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Worldline description of a bi-adjoint scalar and the zeroth copy
Journal of High Energy Physics, 2021 Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective.
Fiorenzo Bastianelli +2 more
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GMOR relation for a QCD-like theory from S-duality
Physics Letters B, 2022 Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an O3 plane and N D3 anti-branes and it realises a USp(2N) ‘electric’ gauge theory with four “quarks” in the two-index ...
Adi Armoni, Henry Harper-Gardner
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Universal Racah matrices and adjoint knot polynomials: Arborescent knots
Physics Letters B, 2016 By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras.
A. Mironov, A. Morozov
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Journal of High Energy Physics, 2018 We construct a 6D nonabelian N=1,0 $$ \mathcal{N}=\left(1,\ 0\right) $$ theory by coupling an N=1,0 $$ \mathcal{N}=\left(1,\ 0\right) $$ tensor multiplet to an N=1,0 $$ \mathcal{N}=\left(1,\ 0\right) $$ hypermultiplet.
Fa-Min Chen
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Asymptotic formulas for a scalar linear delay differential equation
Electronic Journal of Qualitative Theory of Differential Equations, 2016 The linear delay differential equation $$ x'(t)=p(t)x(t-r) $$ is considered, where $r>0$ and the coefficient $p:[t_0,\infty)\to\mathbb{R}$ is a continuous function such that $p(t)\to0$ as $t\to\infty$. In a recent paper [M. Pituk, G. Röst, Bound.
István Győri, Mihály Pituk
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Approximate symmetries of the perturbed KdV-KS equation [PDF]
Iranian Journal of Numerical Analysis and OptimizationThe analysis of approximate symmetries in perturbed nonlinear partial differential equations $(PDEs)$ stands as a cornerstone for unraveling complex physical behaviors and solution patterns.
A. Mohammadpouri +3 more
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