Results 1 to 10 of about 140,543 (167)

Torus knots in adjoint representation and Vogel’s universality [PDF]

European Physical Journal C: Particles and Fields
Vogel’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
doaj   +2 more sources

Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]

Nature Communications
Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Enrico Fontana, Dylan Herman, Shouvanik Chakrabarti, Niraj Kumar, Romina Yalovetzky, Jamie Heredge, Shree Hari Sureshbabu, Marco Pistoia   +7 more
doaj   +2 more sources

A representation for an adjoint operator

Journal of Numerical Analysis and Approximation Theory, 1975
Not available.
Stephen P. Travis
doaj   +3 more sources

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
doaj   +2 more sources

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
doaj   +1 more source

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, Francesco Comberiati, Leonardo de la Cruz   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Gluino Condensation in an Interacting Instanton Ensemble [PDF]

, 2000
We perform a semi-classical study of chiral symmetry breaking and of the spectrum of the Dirac operator in QCD with adjoint fermions. For this purpose we calculate matrix elements of the adjoint Dirac operator between instanton zero modes and study their
A. I. Vainshtein, A. Kovner, A. Ritz, A. V. Smilga, C. G. Callan, D. Amati, D. Amati, D. Diakonov, D. I. Diakonov, D. I. Diakonov, D. Toublan, E. Cohen, E. V. Shuryak, G. C. Rossi, G. Veneziano, G. ’t Hooft, H. Leutwyler, I. Affleck, I. Affleck, I. Affleck, I. Campos, J. C. Osborn, J. Fuchs, J. J. M. Verbaarschot, J. J. M. Verbaarschot, J. W. Negele, K. Intriligator, M. A. Shifman, N. M. Davies, N. Seiberg, R. Kirchner, T. Banks, T. C. Kraan, T. C. Kraan, T. J. Hollowood, T. Schäfer, Thomas Schäfer, U. M. Heller, V. A. Fateev, V. A. Novikov, V. A. Novikov, V. A. Novikov, V. A. Novikov, Y. I. Kogan   +43 more
core   +2 more sources

Representations of hom-Lie algebras [PDF]

, 2012
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail.
A Makhlouf, A Makhlouf, C Chevalley, D Larsson, D Larsson, D Yau, D Yau, D Yau, I Dorfman, J Hartwig, N Jacobson, Y Sheng, Yunhe Sheng   +12 more
core   +1 more source