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Author |
de Azcarraga, J.A.; Fedoruk, S.; Izquierdo, J.M.; Lukierski, J. |
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Title |
Two-twistor particle models and free massive higher spin fields |
Type |
Journal Article |
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Year |
2015 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal  |
J. High Energy Phys. |
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Volume |
04 |
Issue |
4 |
Pages |
010 - 39pp |
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Keywords |
Field Theories in Lower Dimensions; Higher Spin Symmetry; Extended Supersymmetry; Space-Time Symmetries |
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Abstract |
We present D = 3 and D = 4 world-line models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor variables and a second described by a free two-twistor dynamics with constraints. After first quantization in the D = 3 and D = 4 cases, the wave functions satisfying a massive version of Vasiliev's free unfolded equations are given as functions on the SL(2, R) and SL(2, C) group manifolds respectively, which describe arbitrary on-shell momenta and spin degrees of freedom. Further we comment on the D = 6 case, and possible supersymmetric extensions are mentioned as well. Finally, the description of interactions and the Ads/crr duality are briefly considered for massive IHS fields. |
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Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Theoret Phys, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es; |
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Springer |
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English |
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1029-8479 |
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Notes |
WOS:000356852000010 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2293 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M.; Picon, M. |
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Title |
Contractions of Filippov algebras |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
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Volume |
52 |
Issue |
1 |
Pages |
013516 - 24pp |
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Keywords |
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Abstract |
We introduce in this paper the contractions B-c of n-Lie (or Filippov) algebras B and show that they have a semidirect structure as their n = 2 Lie algebra counterparts. As an example, we compute the nontrivial contractions of the simple A(n+1) Filippov algebras. By using the. Inonu-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the B = A(n+1) simple case) the Lie algebras Lie B-c (the Lie algebra of inner endomorphisms of B-c) with certain contractions (Lie B)(IW) and (Lie B)(W-W) of the Lie algebra Lie B associated with B. |
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Address |
[de Azcarraga, Jose A.; Picon, Moises] Univ Valencia, Dept Theoret Phys, E-46100 Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Publisher |
Amer Inst Physics |
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English |
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0022-2488 |
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Notes |
ISI:000286898400034 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
574 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
On a class of n-Leibniz deformations of the simple Filippov algebras |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
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Volume |
52 |
Issue |
2 |
Pages |
023521 - 13pp |
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Keywords |
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Abstract |
We study the problem of infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n > 3 simple finite-dimensional Filippov algebras (FAs) are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n = 2 Filippov (i.e., Lie) algebras. The n = 3 simple FAs, however, admit a nontrivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the n >= 3 simple Filippov algebras do not admit nontrivial central extensions as n-Leibniz algebras of the above class. |
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Address |
[de Azcarraga, Jose A.] Univ Valencia, Dept Theoret Phys, E-46100 Burjassot, Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Publisher |
Amer Inst Physics |
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English |
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ISSN |
0022-2488 |
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Conference |
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Notes |
ISI:000287811800050 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
558 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Mathematical Physics |
Abbreviated Journal |
J. Math. Phys. |
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Volume |
54 |
Issue |
9 |
Pages |
093510 - 14pp |
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Keywords |
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Abstract |
Two types of higher order Lie l-ple systems are introduced in this paper. They are defined by brackets with l > 3 arguments satisfying certain conditions, and generalize the well-known Lie triple systems. One of the generalizations uses a construction that allows us to associate a (2n – 3)-Leibniz algebra pound with a metric n-Leibniz algebra () pound over tilde by using a 2(n – 1)-linear Kasymov trace form for () pound over tilde. Some specific types of k-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie l-ple generalizations reduce to the standard Lie triple systems for l = 3. |
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ISSN |
0022-2488 |
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Conference |
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Notes |
WOS:000325407300032 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
1618 |
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Author |
de Azcarraga, J.A.; Izquierdo, J.M. |
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Title |
n-ary algebras: a review with applications |
Type |
Journal Article |
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Year |
2010 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
43 |
Issue |
29 |
Pages |
293001 - 117pp |
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Keywords |
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Abstract |
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations ( it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A(4) model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. |
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Address |
[de Azcarraga, J. A.] Univ Valencia, Dept Theoret Phys, Fac Phys, E-46100 Valencia, Spain, Email: j.a.de.azcarraga@ific.uv.es |
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Corporate Author |
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Publisher |
Iop Publishing Ltd |
Place of Publication |
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English |
Summary Language |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1751-8113 |
ISBN |
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Notes |
ISI:000279463100003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
419 |
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