scholarly journals Symmetry transformations for square sliced three-way arrays, with applications to their typical rank

2006 ◽  
Vol 418 (1) ◽  
pp. 215-224 ◽  
Author(s):  
Jos M.F. ten Berge ◽  
Alwin Stegeman
Keyword(s):  
Typical Rank ◽  
Symmetry Transformations

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

The typical rank of tall three-way arrays

Psychometrika ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 525-532 ◽  
Author(s):  
Jos M. F. ten Berge
Keyword(s):  
Typical Rank

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

scholarly journals NEW SUPERSTRING ISOMETRIES AND HIDDEN DIMENSIONS

2007 ◽  
Vol 22 (29) ◽  
pp. 5301-5323 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Extra Dimension ◽  
Isometry Group ◽  
Space Time ◽  
Time Dimension ◽  
Superstring Theory ◽  
Symmetry Transformations ◽  
Noncritical Strings ◽  
A Chain ◽  
Symmetry Generators ◽  
Special Space

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ~ H-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology Hn ~ H-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology Hn ~ H-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from Hk ~ H-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO (d, 2) to SO (d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

scholarly journals Dirac masses and mixings in the (geo)SM(EFT) and beyond

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jim Talbert ◽  
Michael Trott
Keyword(s):  
Cp Violation ◽  
Effective Field Theory ◽  
Geometric Realization ◽  
Effective Field ◽  
Renormalization Group Flow ◽  
Quark Masses ◽  
The Standard Model ◽  
Mass Dimension ◽  
Symmetry Transformations ◽  
Group Flow

Abstract We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3×3 Yukawa matrices Y valid when YY† → U†YY†U under global $$ \mathrm{U}{(3)}_{Q_L} $$ U 3 Q L flavour symmetry transformations U. The results apply to the Standard Model Effective Field Theory (SMEFT) and its ‘geometric’ realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the $$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle } $$ 2 H † H /Λ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism’s utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.

scholarly journals LAGRANGIAN APPROACH OF THE FIRST-CLASS CONSTRAINED SYSTEMS

1998 ◽  
Vol 13 (33) ◽  
pp. 2653-2663 ◽  
Author(s):  
YONG-WAN KIM ◽  
YOUNG-JAI PARK ◽  
SEUNG-KOOK KIM
Keyword(s):  
Hamiltonian Formulation ◽  
Constrained Systems ◽  
Lagrangian Approach ◽  
Lagrangian Formalism ◽  
Exact Form ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Local Symmetries

We show how to systematically derive the exact form of local symmetries for the Abelian Proca and CS models, which are converted into first-class constrained systems by the BFT formalism, in the Lagrangian formalism. As a result, without resorting to a Hamiltonian formulation we obtain the well-known U(1) symmetry for the gauge-invariant Proca model, while showing that for the CS model there exist novel symmetries as well as the usual symmetry transformations.

A THEOREM OF SOLÉR, THE THEORY OF SYMMETRY AND QUANTUM MECHANICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260005 ◽  
Author(s):  
GIANNI CASSINELLI ◽  
PEKKA LAHTI
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Logic ◽  
Hilbert Spaces ◽  
Classical Problem ◽  
Partial Solution ◽  
Space Realization ◽  
Symmetry Transformations ◽  
Axiomatic Quantum Mechanics

A classical problem in axiomatic quantum mechanics is deducing a Hilbert space realization for a quantum logic that admits a vector space coordinatization of the Piron–McLaren type. Our aim is to show how a theorem of M. Solér [Characterization of Hilbert spaces by orthomodular spaces, Comm. Algebra23 (1995) 219–243.] can be used to get a (partial) solution of this problem. We first derive a generalization of the Wigner theorem on symmetry transformations that holds already in the Piron–McLaren frame. Then we investigate which conditions on the quantum logic allow the use of Solér's theorem in order to obtain a Hilbert space solution for the coordinatization problem.

scholarly journals CONSTRAINT ALGEBRAS IN GAUGE-INVARIANT SYSTEMS

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV
Keyword(s):  
Wide Class ◽  
Arbitrary Function ◽  
Arbitrary Order ◽  
Local Symmetry ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Constraint Algebra ◽  
Derivatives Of

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.

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