Perturbations of C*-algebraic Invariants
DEFF Research Database (Denmark)
Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.;
2010-01-01
The setting of the article is the so-called theory of perturbations of algebras of operators. It is shown that several of the properties a C*-algebra may have are preseved under pertubations. The main result states that Pisier's concept finite length is a stasble property.......The setting of the article is the so-called theory of perturbations of algebras of operators. It is shown that several of the properties a C*-algebra may have are preseved under pertubations. The main result states that Pisier's concept finite length is a stasble property....
Invariant subvarieties of the 3-tensor space C^2⨂C^2⨂C^2
AGAOKA, Yoshio
1994-01-01
We classify G-invariant subvarieties of the 3-tensor space C^2⨂C^2⨂C^2 that are defined by polynomials with degree≤6,where G=GL(2,C)×GL(2,C)×GL(2,C). We also calculate the character fo S^p(C^2⨂C^2⨂C^2), determine the generators of each irreducible component of S^p(C^2⨂C^2⨂C^2), and obtain some curious identities between them that play a fundamental role in classifying invariant subvarieties.
A Noncrossing Basis for Noncommutative Invariants of SL(2,C)
Lehner, Franz
2009-01-01
Noncommutative invariant theory is a generalization of the classical invariant theory of the action of $SL(2,\\IC)$ on binary forms. The dimensions of the spaces of invariant noncommutative polynomials coincide with the numbers of certain noncrossing partitions. We give an elementary combinatorial explanation of this fact by constructing a noncrossing basis of the homogeneous components. Using the theory free stochastic measures this provides a combinatorial proof of the Molien-Weyl formula in...
RGIsearch: A C++ program for the determination of renormalization group invariants
Verheyen, Rob
2016-05-01
RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the β-functions of quantum field theories, RGIsearch searches for several types of invariants that require different methods. Additionally, it supports the computation of invariants up to two-loop level. A manual for the program is given, including the settings and set-up of the program, as well as a test case.
GL(3,C) invariance of type B 3-fold supersymmetric systems
International Nuclear Information System (INIS)
Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear transformations. In particular, we prove explicitly that the parameter space is transformed as an adjoint representation of it and that every coefficient of the characteristic polynomial appeared in 3-fold superalgebra is algebraic invariants. In the type A case, it includes as a subgroup the GL(2,C) projective transformation studied in the literature. We argue that any N-fold supersymmetric system has a GL(N,C) invariance for an arbitrary integral N
The structure of gauge-invariant ideals of labelled graph $C^*$-algebras
Jeong, Ja A; Park, Gi Hyun
2011-01-01
In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\\mathcal{L},\\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving labelled space $(E,\\mathcal{L},\\mathcal{B})$, where $\\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed graph $E$ with no sinks. Under the assumption that an accommodating set $\\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\\mathcal{L},\\mathcal{B})$. For this, we introduce a quotient labelled space $(E,\\mathcal{L},[\\mathcal{B}]_R)$ arising from an equivalence relation $\\sim_R$ on $\\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\\mathcal{L},[\\mathcal{B}]_R)$ generated by a universal representation of $(E,\\mathcal{L},[\\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\\mathcal{L},[\\m...
d $\\leq$ 1 U d $\\geq$ 25 and W constraints from BRST invariance in the C $\
Gato-Rivera, Beatriz
1992-01-01
The BRST invariance condition in a highest-weight representation of the topological ($\\equiv$ twisted $N=2$) algebra captures the `invariant' content of two-dimensional gravity coupled to matter. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts+matter +`Liouville', while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the `Liouville' differ also by their `ghost numbers', which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge $\\ctop\
Cosmetic surgery and the $SL(2,\\mathbb{C})$ Casson invariant for two-bridge knots
Ichihara, Kazuhiro; Saito, Toshio
2016-01-01
We consider the cosmetic surgery problem for two-bridge knots in the 3-sphere. It is seen that all the two-bridge knots at most 9 crossings other than $9_{27} = S(49,19)=C[2,2,-2,2,2,-2]$ admits no purely cosmetic surgery pairs. Then we show that any two-bridge knot of the Conway form $[2x,2,-2x,2x,2,-2x]$ with $x \\ge 1$ admits no cosmetic surgery pairs yielding homology 3-spheres, where $9_{27}$ appears for $x=1$. Our advantage to prove this is using the $SL(2,\\mathbb{C})$ Casson invariant.
Time-reversal-invariance-violating nucleon-nucleon potential in the 1/N_c expansion
Samart, Daris; Schindler, Matthias R; Phillips, Daniel R
2016-01-01
We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H
2003-02-24
A wide range of 1D shape invariant potentials lie in two different classes. In either of these classes the quantum states are distinguished by both of the main and the secondary quantum numbers n and m. We show that quantum states of the first and of the second classes represent shape invariance with respect to n and m, respectively. We also analyze the relationship between these two classes with Lie algebra sl(2,c)
Fakhri, H.
2003-02-01
A wide range of 1D shape invariant potentials lie in two different classes. In either of these classes the quantum states are distinguished by both of the main and the secondary quantum numbers n and m. We show that quantum states of the first and of the second classes represent shape invariance with respect to n and m, respectively. We also analyze the relationship between these two classes with Lie algebra sl(2, c).
Analysis of the dilepton invariant mass spectrum in C + C collisions at 2A and 1A GeV
International Nuclear Information System (INIS)
Recently the HADES Collaboration has published the invariant mass spectrum of e+e- pairs, dN/dMe+e-, produced in C + C collisions at 2A GeV. Using electromagnetic probes, one hopes to get information from this experiment on hadron properties at high density and temperature. Simulations show that firm conclusions on possible in-medium modifications of meson properties will only be possible when the elementary meson production cross sections, especially in the pn channel, as well as production cross sections of baryonic resonances are better known. Presently one can conclude that (i) simulations overpredict by far the cross section at Me+e-≅Mω0 if free production cross sections are used and that (ii) the upper limit of the η decay into e+e- is smaller than the present upper limit of the Particle Data Group. This is the result of simulations using the isospin quantum molecular dynamics approach
Analysis of dilepton invariant mass spectrum in C+C at 2 and 1 AGeV
International Nuclear Information System (INIS)
Recently the HADES collaboration has published the invariant mass spectrum of e+e- pairs, dN/dMe+e-, produced in C+C collisions at 2 AGeV. Using electromagnetic probes, one hopes to get in this experiment information on hadron properties at high density and temperature. Simulations show that firm conclusions on possible in-medium modifications of meson properties will only be possible when the elementary meson production cross sections, especially in the pn channel, as well as production cross sections of baryonic resonances are better known. Presently one can conclude that a) simulations over-predict by far the cross section at Me+e- ≅ Mω0 if free production cross sections are used and that b) the upper limit of the η decay into e+e- is smaller than the present upper limit of the Particle Data Group. This is the result of simulations using the Isospin Quantum Molecular Dynamics (IQMD) approach. (authors)
Matching of gauge invariant dimension 6 operators for $b\\to s$ and $b\\to c$ transitions
Aebischer, Jason; Fael, Matteo; Greub, Christoph
2015-01-01
New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the $SU(3)_C \\times SU(2)_L \\times U(1)_Y$ gauge invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for $b \\to s$ and $b\\to c$ transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, $W$, $Z$ and the Higgs particle. We first carry out the matching of the dim-6 operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter $b \\to s$ transitions already at tree level, but can give relevant one-loop matching effects.
Matching of gauge invariant dimension-six operators for b → s and b → c transitions
Aebischer, Jason; Crivellin, Andreas; Fael, Matteo; Greub, Christoph
2016-05-01
New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are in-variant under the Standard Model gauge group. In this article, we study the matching of the SU(3) C × SU(2) L × U(1) Y gauge invariant dimension-six operators on the standard B physics Hamiltonian relevant for b → s and b → c transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, W , Z and the Higgs particle. We first carry out the matching of the dimension-six operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter b → s transitions already at tree level, but can give relevant one-loop matching effects.
R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C Invariant Spin Chain
Directory of Open Access Journals (Sweden)
Sergey É. Derkachov
2006-12-01
Full Text Available The problem of constructing the SL(N,C invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators for arbitrarily principal series representations of SL(N,C are obtained in an explicit form. We construct the commutative family of the operators Q_k(u which can be identified with the Baxter operators for the noncompact SL(N,C spin magnet.
International Nuclear Information System (INIS)
We consider local unitary invariants and entanglement monotones for the mixed two qutrit system. Character methods for the local SU(3) × SU(3) transformation group are used to establish the count of algebraically independent polynomial invariants up to degree 5 in the components of the density operator. These are identified up to quartic degree in the standard basis of Gell–Mann matrices, with the help of the calculus of f and d coefficients. Next, investigating local measurement operations, we study a SLOCC qutrit group, which plays the role of a ‘relativistic’ transformation group analogous to that of the Lorentz group SL(2,C)R≃SO(3,1) for the qubit case. This is the group SL(3,C)R, presented as a group of real 9 × 9 matrices acting linearly on the nine-dimensional space of projective coordinates for the qutrit density matrix. The counterpart, for qutrits, of the invariant 4 × 4 Minkowski metric of the qubit case, proves to be a certain 9 × 9 × 9 totally symmetric three-fold tensor generalizing the Gell–Mann d coefficient. Using this structure, we provide a count of the corresponding local special linear polynomial invariants using group character methods. Finally, we give an explicit construction of the lowest degree quantity (the cubic invariant) and its expansion in terms of SU(3) × SU(3) invariants, and we indicate how to construct higher degree analogues. These quantities are proven to yield entanglement monotones. This work generalizes and partly extends the paper of King et al (2007 J. Phys. A: Math. Theor. 40 10083) on the mixed two qubit system, which is reviewed in an appendix. (paper)
Search for Violations of Lorentz Invariance and C P T Symmetry in B(s) 0 Mixing
Aaij, R.; Abellán Beteta, C.; Adeva, B.; Adinolfi, M.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; d'Argent, P.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baker, S.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Bellee, V.; Belloli, N.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Betti, F.; Bettler, M.-O.; van Beuzekom, M.; Bifani, S.; Billoir, P.; Bird, T.; Birnkraut, A.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borgheresi, A.; Borghi, S.; Borisyak, M.; Borsato, M.; Boubdir, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Britsch, M.; Britton, T.; Brodzicka, J.; Buchanan, E.; Burr, C.; Bursche, A.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Calvi, M.; Calvo Gomez, M.; Campana, P.; Campora Perez, D.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cauet, Ch.; Cavallero, G.; Cenci, R.; Charles, M.; Charpentier, Ph.; Chatzikonstantinidis, G.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chrzaszcz, M.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coco, V.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collazuol, G.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombes, M.; Coquereau, S.; Corti, G.; Corvo, M.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A.; Cruz Torres, M.; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dall'Occo, E.; Dalseno, J.; David, P. N. Y.; Davis, A.; De Aguiar Francisco, O.; De Bruyn, K.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Simone, P.; Dean, C.-T.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Déléage, N.; Demmer, M.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Di Ruscio, F.; Dijkstra, H.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Dungs, K.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; El Rifai, I.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Färber, C.; Farley, N.; Farry, S.; Fay, R.; Fazzini, D.; Ferguson, D.; Fernandez Albor, V.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fleuret, F.; Fohl, K.; Fontana, M.; Fontanelli, F.; Forshaw, D. C.; Forty, R.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Garsed, P. J.; Gascon, D.; Gaspar, C.; Gavardi, L.; Gazzoni, G.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianı, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gligorov, V. V.; Göbel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Griffith, P.; Grillo, L.; Grünberg, O.; Gushchin, E.; Guz, Yu.; Gys, T.; Hadavizadeh, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hall, S.; Hamilton, B.; Han, X.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; He, J.; Head, T.; Heister, A.; Hennessy, K.; Henrard, P.; Henry, L.; Hernando Morata, J. A.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hoballah, M.; Hombach, C.; Hongming, L.; Hulsbergen, W.; Humair, T.; Hushchyn, M.; Hussain, N.; Hutchcroft, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Karodia, S.; Kecke, M.; Kelsey, M.; Kenyon, I. R.; Kenzie, M.; Ketel, T.; Khairullin, E.; Khanji, B.; Khurewathanakul, C.; Kirn, T.; Klaver, S.; Klimaszewski, K.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Kozeiha, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krokovny, P.; Kruse, F.; Krzemien, W.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kuonen, A. K.; Kurek, K.; Kvaratskheliya, T.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lanfranchi, G.; Langenbruch, C.; Langhans, B.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.-P.; Lefèvre, R.; Leflat, A.; Lefrançois, J.; Lemos Cid, E.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Liu, X.; Loh, D.; Longstaff, I.; Lopes, J. H.; Lucchesi, D.; Lucio Martinez, M.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Lusardi, N.; Lusiani, A.; Lyu, X.; Machefert, F.; Maciuc, F.; Maev, O.; Maguire, K.; Malde, S.; Malinin, A.; Manca, G.; Mancinelli, G.; Manning, P.; Mapelli, A.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marino, P.; Marks, J.; Martellotti, G.; Martin, M.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massacrier, L. M.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Mauri, A.; Maurin, B.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Melnychuk, D.; Merk, M.; Merli, A.; Michielin, E.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Molina Rodriguez, J.; Monroy, I. A.; Monteil, S.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Morris, A. B.; Mountain, R.; Muheim, F.; Müller, D.; Müller, J.; Müller, K.; Müller, V.; Mussini, M.; Muster, B.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen-Mau, C.; Niess, V.; Nieswand, S.; Niet, R.; Nikitin, N.; Nikodem, T.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Onderwater, C. J. G.; Osorio Rodrigues, B.; Otalora Goicochea, J. M.; Otto, A.; Owen, P.; Oyanguren, A.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Pappenheimer, C.; Parker, W.; Parkes, C.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pikies, M.; Pinci, D.; Pistone, A.; Piucci, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Price, E.; Price, J. D.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Quagliani, R.; Rachwal, B.; Rademacker, J. H.; Rama, M.; Ramos Pernas, M.; Rangel, M. S.; Raniuk, I.; Raven, G.; Redi, F.; Reichert, S.; dos Reis, A. C.; Renaudin, V.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Rogozhnikov, A.; Roiser, S.; Romanovsky, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Ruf, T.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santimaria, M.; Santovetti, E.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schael, S.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Sergi, A.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Siddi, B. G.; Silva Coutinho, R.; Silva de Oliveira, L.; Simi, G.; Sirendi, M.; Skidmore, N.; Skwarnicki, T.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Soomro, F.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Stefkova, S.; Steinkamp, O.; Stenyakin, O.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Sun, L.; Sutcliffe, W.; Swientek, K.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szumlak, T.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Traill, M.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valat, S.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vázquez Sierra, C.; Vecchi, S.; van Veghel, M.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Volkov, V.; Vollhardt, A.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wicht, J.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Williams, T.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wraight, K.; Wright, S.; Wyllie, K.; Xie, Y.; Xu, Z.; Yang, Z.; Yin, H.; Yu, J.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhelezov, A.; Zheng, Y.; Zhokhov, A.; Zhong, L.; Zhukov, V.; Zucchelli, S.; LHCb Collaboration
2016-06-01
Violations of C P T symmetry and Lorentz invariance are searched for by studying interference effects in B0 mixing and in Bs0 mixing. Samples of B0→J /ψ KS0 and Bs0→J /ψ K+K- decays are recorded by the LHCb detector in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb-1 . No periodic variations of the particle-antiparticle mass differences are found, consistent with Lorentz invariance and C P T symmetry. Results are expressed in terms of the standard model extension parameter Δ aμ with precisions of O (10-15) and O (10-14) GeV for the B0 and Bs0 systems, respectively. With no assumption on Lorentz (non)invariance, the C P T -violating parameter z in the Bs0 system is measured for the first time and found to be R e (z ) =-0.022 ±0.033 ±0.005 and I m (z ) =0.004 ±0.011 ±0.002 , where the first uncertainties are statistical and the second systematic.
Speak, Anneliese O; Platt, Nicholas; Salio, Mariolina; te Vruchte, Danielle Taylor; Smith, David A.; Shepherd, Dawn; Veerapen, Natacha; Besra, Gurdyal; Yanjanin, Nicole M.; Simmons, Louise; Imrie, Jackie; Wraith, James E.; Lachmann, Robin; Hartung, Ralf; Runz, Heiko
2012-01-01
Invariant Natural Killer T (iNKT) cells are a specialised subset of T cells that are restricted to the MHC class I like molecule, CD1d. The ligands for iNKT cells are lipids, with the canonical superagonist being α-galactosylceramide, a non-mammalian glycosphingolipid. Trafficking of CD1d through the lysosome is required for the development of murine iNKT cells. Niemann-Pick type C (NPC) disease is a lysosomal storage disorder caused by dysfunction in either of two lysosomal proteins, NPC1 or...
Lunar Laser Ranging Test of the Invariance of c: a Correction
Directory of Open Access Journals (Sweden)
Bruchholz U. E.
2010-10-01
Full Text Available In the APOLLO test, a speed of light was found, which seemingly supports a Galileian addition theorem of velocities. However, the reported difference of 200 +/- 10 m/s is based on a simple error. The correct evaluation of this test leads to the known value of c within the given precision. This correction does not mean an impossibility of detecting spatial anisotropies or gravitational waves.
Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant
DEFF Research Database (Denmark)
Eilers, Søren; Loring, Terry A.; Pedersen, Gert Kjærgård
1999-01-01
varying severity, on the given vertical maps and describe the solutions in terms of push-outs and pull-backs of certain diagrams. Our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products. This leads to new results about the K......-theory of amalgamated free products, verifying the Cuntz conjecture in certain cases. We also obtain new results about extensions of matricial fieldC*-algebras, verifying partially a conjecture of Blackadar and Kirchberg. Finally, we show that almost commuting unitary matrices can be uniformly approximated...
Li, Jun; Guo, Hua
2015-12-01
The permutation invariant polynomial-neural network (PIP-NN) approach is extended to fit intermolecular potential energy surfaces (PESs). Specifically, three PESs were constructed for the Ne-C2H2 system. PES1 is a full nine-dimensional PIP-NN PES directly fitted to ˜42 000 ab initio points calculated at the level of CCSD(T)-F12a/cc-pCVTZ-F12, while the other two consist of the six-dimensional PES for C2H2 [H. Han, A. Li, and H. Guo, J. Chem. Phys. 141, 244312 (2014)] and an intermolecular PES represented in either the PIP (PES2) or PIP-NN (PES3) form. The comparison of fitting errors and their distributions, one-dimensional cuts and two-dimensional contour plots of the PESs, as well as classical trajectory collisional energy transfer dynamics calculations shows that the three PESs are very similar. We conclude that full-dimensional PESs for non-covalent interacting molecular systems can be constructed efficiently and accurately by the PIP-NN approach for both the constituent molecules and intermolecular parts.
Galilei invariant molecular dynamics
International Nuclear Information System (INIS)
We construct a C*-dynamical model for a chemical reaction. Galilei invariance of our nonrelativistic model is demonstrated by defining it directly on a Galilean space-time fibrebundle with C*-algebra valued fibre, i.e. without reference to any coordinate system. The existence of equilibrium states in this model is established and some of their properties are discussed. (orig.)
Illumination Invariant Unsupervised Segmenter
Czech Academy of Sciences Publication Activity Database
Haindl, Michal; Mikeš, Stanislav; Vácha, Pavel
Los Alamitos : IEEE, 2009, s. 4025-4028. ISBN 978-1-4244-5655-0. ISSN 1522-4880. [ICIP 2009. Cairo (EG), 07.11.2009-11.11.2009] R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : unsupervised image segmentation * Illumination Invariants Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2009/RO/haindl-illumination invariant unsupervised segmenter.pdf
Current forms and gauge invariance
International Nuclear Information System (INIS)
Let C be the bundle of connections of a principal G-bundle π:P → M, and let V be the vector bundle associated with P by a linear representation G → GL(V) on a finite-dimensional vector space V. The Lagrangians on J1(C x MV) whose current form is gauge invariant, are described and the gauge-invariant Lagrangians on J1(V) are classified
Luo, Yiqi; Sims, Daniel A.; Thomas, Richard B.; Tissue, David T.; Ball, J. Timothy
1996-06-01
Rising atmospheric CO2 concentration (Ca) may alter two components (sensitivity and acclimation) of global photosynthetic carbon influx into terrestrial ecosystems (PG). Most existing global models focus on long-term acclimation. We have developed a leaf-level function (ℒ) to quantify short-term increment of PG associated with sensitivity. The ℒ function is the normalized response of leaf photosynthesis to a small change in Ca and has been suggested to be an invariant function for C3 plants grown in diverse environments. This paper tests the hypothesis that ℒ is an invariant function. We calculated values of ℒ from 9 sets of experimental data which incorporated photosynthetic responses of 12 plant species to measurement conditions of light and temperature and to growth in different light, temperature, nitrogen, phosphorus, water stress, and CO2 concentration. Absolute rates of leaf photosynthesis differed by more than tenfold due to species differences and environmental variation. However, ℒ values derived from these data sets converged into a narrow range defined by two equations of the ℒ function, confirming that ℒ was insensitive to differences in photosynthetic capacity among species and between plants acclimated to different growth environments. Using the ℒ function, we predict that a yearly increase of 1.5 parts per million (ppm) in Ca will induce an increase in PG by 0.18 to 0.34 Gt (1 Gt = 1015 g) C yr-1 in 1993, provided that (1) PG = 120 Gt C yr-1, (2) 85% of PG is generated by C3 plant assimilation, and (3) the 1.5-ppm increase in Ca will not induce significant photosynthetic acclimation.
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Meyer, Mathieu; Schuett, Carsten; Werner, Elisabeth M.
2013-01-01
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)} denotes the polar of K with respect to p(K). We investigate which affine invariant points do have a dual point, whether this ...
Attractiveness of Invariant Manifolds
Pei, Lijun
2011-01-01
In this paper an operable, universal and simple theory on the attractiveness of the invariant manifolds is first obtained. It is motivated by the Lyapunov direct method. It means that for any point $\\overrightarrow{x}$ in the invariant manifold $M$, $n(\\overrightarrow{x})$ is the normal passing by $\\overrightarrow{x}$, and $\\forall \\overrightarrow{x^{'}} \\in n(\\overrightarrow{x})$, if the tangent $f(\\overrightarrow{x^{'}})$ of the orbits of the dynamical system intersects at obtuse (sharp) angle with the normal $n(\\overrightarrow{x})$, or the inner product of the normal vector $\\overrightarrow{n}(\\overrightarrow{x})$ and tangent vector $\\overrightarrow{f}(\\overrightarrow{x^{'}})$ is negative (positive), i.e., $\\overrightarrow{f}(\\overrightarrow{x^{'}}). \\overrightarrow{n}(\\overrightarrow{x}) )0$, then the invariant manifold $M$ is attractive (repulsive). Some illustrative examples of the invariant manifolds, such as equilibria, periodic solution, stable and unstable manifolds, other invariant manifold are pre...
Molecular invariants: atomic group valence
International Nuclear Information System (INIS)
Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author)
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
Relativistic gauge invariant potentials
International Nuclear Information System (INIS)
A global method characterizing the invariant connections on an abelian principal bundle under a group of transformations is applied in order to get gauge invariant electromagnetic (elm.) potentials in a systematic way. So, we have classified all the elm. gauge invariant potentials under the Poincare subgroups of dimensions 4, 5, and 6, up to conjugation. It is paid attention in particular to the situation where these subgroups do not act transitively on the space-time manifold. We have used the same procedure for some galilean subgroups to get nonrelativistic potentials and study the way they are related to their relativistic partners by means of contractions. Some conformal gauge invariant potentials have also been derived and considered when they are seen as consequence of an enlargement of the Poincare symmetries. (orig.)
Wu, Pei-Chen
2010-01-01
This study examined measurement invariance (i.e., configural invariance, metric invariance, scalar invariance) of the Chinese version of Beck Depression Inventory II (BDI-II-C) across college males and females and compared gender differences on depression at the latent factor mean level. Two samples composed of 402 male college students and 595…
Transformation invariant sparse coding
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel Nørgaard
2011-01-01
Sparse coding is a well established principle for unsupervised learning. Traditionally, features are extracted in sparse coding in specific locations, however, often we would prefer invariant representation. This paper introduces a general transformation invariant sparse coding (TISC) model. The...... model decomposes images into features invariant to location and general transformation by a set of specified operators as well as a sparse coding matrix indicating where and to what degree in the original image these features are present. The TISC model is in general overcomplete and we therefore invoke...... sparse coding to estimate its parameters. We demonstrate how the model can correctly identify components of non-trivial artificial as well as real image data. Thus, the model is capable of reducing feature redundancies in terms of pre-specified transformations improving the component identification....
NIMET PANCAROGLU; FATIH NURAY
2013-01-01
In this paper, we define invariant convergence, lacunary invariant convergence, invariant statistical convergence, lacunary invariant statistical convergence for sequences of sets. We investigate some relations between lacunary invariant statistical convergence and invariant statistical convergence for sequences of sets.
Pérez-Nadal, Guillem
2016-01-01
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates "scaling like time" is generically greater than one. We propose the Cartesian product of two curved spaces, with the metric of each space parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry.
Kameko, Masaki
2012-01-01
For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the classifying space of its maximal torus is an epimorphism except for the case $p=3$, $G=E_8$.
Relativistically invariant quantum information
Bartlett, Stephen D.; Terno, Daniel R.
2004-01-01
We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz reference frame. Such relativistically invariant quantum information is free of the difficulties associated with encoding into spin or other degrees of freedom in a relativistic context.
Modular invariant gaugino condensation
International Nuclear Information System (INIS)
The construction of effective supergravity lagrangians for gaugino condensation is reviewed and recent results are presented that are consistent with modular invariance and yield a positive definite potential of the noscale type. Possible implications for phenomenology are briefly discussed. 29 refs
Wetterich, C
2016-01-01
We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.
Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko
2016-08-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
Modifications of Paroemia Invariants
Directory of Open Access Journals (Sweden)
Taliya F. Pecherskikh
2013-01-01
Full Text Available The phenomenon of modifications of paroemia invariants proves that language constantly changes and develops. The realization of communication need through the new evocative forms of expression is generality of the opposite linguistic phenomena of occasional variants of paroemia, aimed at the establishment of equilibrium in phraseology.
Kobayashi, Tatsuo; Urakawa, Yuko
2016-01-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field $T$ whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by $T$. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential $V_{ht}$, but it also has a non-negligible deviation from $V_{ht}$. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still po...
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Continuous Integrated Invariant Inference Project
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Invariant types in NIP theories
Simon, Pierre
2014-01-01
We study invariant types in NIP theories. Amongst other things: we prove a definable version of the (p,q)-theorem in theories of small or medium directionality; we construct a canonical retraction from the space of M-invariant types to that of M-finitely satisfiable types; we show some amalgamation results for invariant types and list a number of open questions.
Permutationally invariant state reconstruction
Moroder, Tobias; Toth, Geza; Schwemmer, Christian; Niggebaum, Alexander; Gaile, Stefanie; Gühne, Otfried; Weinfurter, Harald
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed n...
Invariants for Parallel Mapping
Institute of Scientific and Technical Information of China (English)
YIN Yajun; WU Jiye; FAN Qinshan; HUANG Kezhi
2009-01-01
This paper analyzes the geometric quantities that remain unchanged during parallel mapping (i.e., mapping from a reference curved surface to a parallel surface with identical normal direction). The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invadants or geometri-cally conserved quantities. These include not only local mapping invadants but also global mapping invari-ants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invadants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invadants and transformations have potential applications in geometry, physics, biome-chanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.
Geometric local invariants and pure three-qubit states
International Nuclear Information System (INIS)
We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or ''gauge'' invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters, and the gauge invariant observable associated with a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link transformations between the qubits are defined by the correlations between them, and the gauge invariant observable, the local invariants associated with a particular closed path, are also given by a Wilson looplike construction. The link transformations share many of the properties of parallel transporters, although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three-qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way; however, the framework given here is applicable to generating local unitary invariants for mixed states composed of any number of d-level quantum systems. We give an operational interpretation of these invariants in terms of observables.
Conformal invariance in supergravity
International Nuclear Information System (INIS)
In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)
Braaten, Eric
2015-01-01
XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D*0 --> D0 pi0. The transitions D*0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D*0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D*0 propagator and for the D*0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.
Cheng, Miranda C N; Harrison, Sarah M; Kachru, Shamit
2015-01-01
In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz--Klemm--Vafa (KKV), and Katz--Klemm--Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway's group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel--Hoheneg...
Invariant operators of inhomogeneous groups
International Nuclear Information System (INIS)
The problems concerning the invariant operators of the W(p, q) Weyl group of arbitrary dimension are considered. The Weyl group relative invariants, which do not contain the dilatation operators and which are the absolute invariants of the ISO (p, q) group, are searched for. The invariant operators of the Weyl group are represented in the form of the ratio of the Cazimir operators of the inhomogeneous pseudoorthogonal subgroup. It is shown that all the invariant operators of the W(p, q) Weyl group are rational and their number is [p+q-1/2
Conformally Invariant Off-shell Strings
Myers, R C
1993-01-01
Recent advances in non-critical string theory allow a unique continuation of critical Polyakov string amplitudes to off-shell momenta, while preserving conformal invariance. These continuations possess unusual, apparently stringy, characteristics, as we illustrate with our results for three-point functions. (Talk by R.C.M. at Strings '93)
Illumination Invariants Based on Markov Random Fields
Czech Academy of Sciences Publication Activity Database
Vácha, Pavel; Haindl, Michal
Vukovar, Croatia : In-Teh, 2010 - (Herout, A.), s. 253-272 ISBN 978-953-7619-90-9 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : illumination invariants * textural features * Markov random fields Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2010/RO/vacha-illumination invariants based on markov random fields.pdf
Thinning Invariant Partition Structures
Starr, Shannon
2011-01-01
A partition structure is a random point process on $[0,1]$ whose points sum to 1, almost surely. In the case that there are infinitely many points to begin with, we consider a thinning action by: first, removing points independently, such that each point survives with probability $p>0$; and, secondly, rescaling the remaining points by an overall factor to normalize the sum again to 1. We prove that the partition structures which are "thinning divisible" for a sequence of $p$'s converging to 0 are mixtures of the Poisson-Kingman partition structures. We also consider the property of being "thinning invariant" for all $p \\in (0,1)$.
Anistropic Invariant FRW Cosmology
Chagoya, J F
2015-01-01
In this paper we study the effects of including anisotropic scaling invariance in the minisuperspace Lagrangian for a universe modelled by the Friedman-Robertson-Walker metric, a massless scalar field and cosmological constant. We find that canonical quantization of this system leads to a Schroedinger type equation, thus avoiding the frozen time problem of the usual Wheeler-DeWitt equation. Furthermore, we find numerical solutions for the classical equations of motion, and we also find evidence that under some conditions the big bang singularity is avoided in this model.
Lorentz-invariant non-commutative QED
International Nuclear Information System (INIS)
Lorentz-invariant non-commutative QED (NCQED) is constructed so as to be a part of the Lorentz-invariant non-commutative Standard Model (NCSM), a subject to be treated in later publications. Our NCSM is based on Connes' observation that the total fermion field in the Standard Model can be regarded as a bi-module over a flavor-color algebra. In this paper, it is shown that there exist two massless gauge fields in NCQED that are interchanged by the C' transformation. Since C' is reduced to the conventional charge conjugation C in the commutative limit, in the same limit, the two gauge fields become identical to the photon field which couples to only four spinors, with charges ±2, ±1. Following Carlson, Carone and Zobin, our NCQED respects Lorentz invariance, employing the Doplicher-Fredenhagen-Roberts algebra instead of the usual algebra with constant θμν. In the new version, θμν becomes an integration variable. We show, using a simple NC scalar model, that the θ integration yields an invariant damping factor instead of the oscillating one in the nonplanar self-energy diagram in the one-loop approximation. The Seiberg-Witten map shows that the θ expansion of NCQED generates exotic but well-motivated derivative interactions beyond QED, with allowed charges being only 0, ±1, ±2. (author)
Tractors, mass, and Weyl invariance
International Nuclear Information System (INIS)
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus-a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories-which rely on the interplay between mass and gauge invariance-are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s≤2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s≥2 we give tractor equations of motion unifying massive, massless, and partially massless theories
On obtaining strictly invariant Lagrangians from gauge-invariant Lagrangians
International Nuclear Information System (INIS)
Lagrangian dynamical systems are considered on tangent bundles of differentiable manifolds whose Lagrangian functions are gauge invariant under the action of a Lie group on the base manifold. Necessary and sufficient conditions are then obtained for finding a function on the base manifold whose time derivative, if added to the gauge-invariant Lagrangian, yields a strictly invariant one. The problem is transported from the tangent bundle also to the cotangent bundle
Invariants for minimal conformal supergravity in six dimensions
Butter, Daniel; Novak, Joseph; Theisen, Stefan
2016-01-01
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D ${\\cal N} = (1, 0)$ superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D ${\\cal N} = (1, 0)$ conformal supergravity, which contain $C^3$ and $C\\Box C$ terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric $F \\Box F$ invariant in curved superspace.
Palmer, T N
2016-01-01
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$ is treated as a deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. In this approach, the geometry of $I_U$, and not a set of differential evolution equations in space-time $\\mathcal M_U$, provides the most primitive description of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is based on Cantor sets of space-time trajectories in state space, homeomorphic to the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the non-commutativity of position and momentum observables arises from number theory - in particular the non-commensurateness of $\\phi$ and $\\cos \\phi$. The complex Hilbert Space and the relativistic Dirac Equation respectively are shown to describe $I_U$...
Viability, invariance and applications
Carja, Ovidiu; Vrabie, Ioan I
2007-01-01
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza;
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti......Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large......-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum...... likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex...
Polynomial invariants of quantum codes
Rains, E M
1997-01-01
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial invariants. We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence with S_k^n. We then present a number of equations and inequalities in these invariants; in particular, we give a higher-order generalization of the shadow enumerator of a code, and prove that its coefficients are nonnegative. We also prove that the quartic invariants of a ((4,4,2)) are uniquely determined, an important step in a proof that any ((4,4,2)) is additive ([2]).
Tractors, Mass and Weyl Invariance
Gover, A R; Waldron, A
2008-01-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus--a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner--Freedman stability bounds for Anti de Sitter theories arise na...
Factorization invariants in numerical monoids
O'Neill, Christopher; Pelayo, Roberto
2015-01-01
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids of the natural numbers), several factorization invariants have received much attention in the recent literature. In this survey article, we give an overview of the length set, elasticity, delta set, $\\omega$-primality, and catenary degree invariants in the ...
Invariants and Likelihood Ratio Statistics
McCullagh, P.; Cox, D. R.
1986-01-01
Because the likelihood ratio statistic is invariant under reparameterization, it is possible to make a large-sample expansion of the statistic itself and of its expectation in terms of invariants. In particular, the Bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log-likelihood derivatives. Such expansions are given, first for a scalar parameter and then for vector parameters. Geometrical interpretation is given where possible and s...
Tractors, mass, and Weyl invariance
Gover, A. R.; Shaukat, A.; Waldron, A.
2009-05-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s⩽2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s⩾2 we give tractor equations of motion unifying massive, massless, and partially massless theories.
Topological invariants in magnetic hydrodynaics
International Nuclear Information System (INIS)
A definition of force line reconnection is proposed within the framework of the ideal hydrodynamics (Rem > 1). It detailizes some previous results. On the basis of the definition it is proved that the asymptotic Hopf invariant is conserved within a time interval τ which is much smaller than the skin (diffusion) time τd. Generally speaking there are no other invariants characterizing a magnetic field configuration (in simply-connected domains). For smooth flow of an ideally conducting fluid (Rem=∞) a method is proposed for determining the linked force line invariants which differ from the Hopf invariant
Conformal Invariant Teleparallel Cosmology
Momeni, Davood
2014-01-01
Teleparallel gravities revisited under conformal transformations. We find several kinds of the Lagrangians, all invariant under conformal transformation. Motivated by observational data,we investigate FRW cosmological solutions in the vacuum. To include the matter fields,we mention that we have few possibilities for our matter Lagrangian to respect the conformal symmetry. FRW equations,have been derived in terms of the effective energy and pressure components. In vacuum we find an exact solution for Hubble parameter which is compatible with the observational data but it is valid only in the range of $z\\ge 0.07$. Scalar torsion models in which we have the extra scalar field is examined under FRW spacetime. We introduce the potential term $\\frac{1}{4!}\\mu\\phi^4$ as the minimal self interaction with conformal symmetry.
Lorentz invariant intrinsic decoherence
Milburn, G J
2003-01-01
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum grav...
Invariants of Lagrangian surfaces
Yau, Mei-Lin
2004-01-01
We define a nonnegative integer $\\la(L,L_0;\\phi)$ for a pair of diffeomorphic closed Lagrangian surfaces $L_0,L$ embedded in a symplectic 4-manifold $(M,\\w)$ and a diffeomorphism $\\phi\\in\\Diff^+(M)$ satisfying $\\phi(L_0)=L$. We prove that if there exists $\\phi\\in\\Diff^+_o(M)$ with $\\phi(L_0)=L$ and $\\la(L,L_0;\\phi)=0$, then $L_0,L$ are symplectomorphic. We also define a second invariant $n(L_1,L_0;[L_t])=n(L_1,L_0,[\\phi_t])$ for a smooth isotopy $L_t=\\phi_t(L_0)$ between two Lagrangian surfac...
International Nuclear Information System (INIS)
Let ZLMO be the 3-manifold invariant of [LMO]. It is shown that ZLMO(M) = 1, if the first Betti number of M, b1 (M), is greater than 3. If b1 (M) = 3, then ZLMO (M) is completely determined by the cohomology ring of M. A relation of ZLMO with the Rozansky-Witten invariants ZXRW[M] is established at a physical level of rigour. We show that ZXRW[M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant. (author)
Chiral Invariance of Massive Fermions
Das, A.(University of Arizona, Tucson, AZ, 85721, USA); Hott, M
1994-01-01
We show that a massive fermion theory, while not invariant under the conventional chiral transformation, is invariant under a $m$-deformed chiral transformation. These transformations and the associated conserved charges are nonlocal but reduce to the usual transformations and charges when $m=0$. The $m$-deformed charges commute with helicity and satisfy the conventional chiral algebra.
Reducing Lookups for Invariant Checking
DEFF Research Database (Denmark)
Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just;
2013-01-01
satisfied. We present a formal model of this scenario, based on a simple query language for the expression of invariants that covers the core of a realistic query language. We present an algorithm which simplifies a representation of the invariant, along with a mechanically verified proof of correctness. We...
Multilocal invariants for the classical groups
Directory of Open Access Journals (Sweden)
Paul F. Dhooghe
2003-01-01
Full Text Available Multilocal higher-order invariants, which are higher-order invariants defined at distinct points of representation space, for the classical groups are derived in a systematic way. The basic invariants for the classical groups are the well-known polynomial or rational invariants as derived from the Capelli identities. Higher-order invariants are then constructed from the former ones by means of total derivatives. At each order, it appears that the invariants obtained in this way do not generate all invariants. The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.
Fayngold, Moses
2010-01-01
A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as relativistic invariants under space-time rotations. Only observables in the first three categories are authentic invariants, whereas the single "invariant" - proper length - in the fourth category is actually not an invariant. The proper length has little is anything to do with proper distance which is a true invariant. On the other hand, proper distance, proper time, and rest mass have more in common than usually recognized, and particularly, mass - time analogy opens another view of the twin paradox.
Invariant Measures for Cherry Flows
Saghin, Radu; Vargas, Edson
2013-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Hidden scale invariance of metals
DEFF Research Database (Denmark)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.;
2015-01-01
of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were......Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...
Physical Invariants of Intelligence
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
Neutrinos superluminality and Local Lorentz Invariance
Cardone, F; Petrucci, A
2011-01-01
The recent measurement of the neutrino velocity with the OPERA detector in the CNGS beam, on whose basis it was found that (v-c)/c = (2.48 \\pm 0.28 (stat.) \\pm 0.30 (sys.)) 10e-5, does not contain any significant violation of Local Lorentz Invariance (LLI), since the corresponding value of the parameter delta=(u/c)^2-1, that represents the upper limit of the breakdown of LLI, is at least three orders of magnitude higher than the known lower limit reported in literature and is compatible with the values estimated by other experiments carried out so far.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems. PMID:26428557
Invariants of Toric Seiberg Duality
Hanany, Amihay; Jejjala, Vishnu; Pasukonis, Jurgis; Ramgoolam, Sanjaye; Rodriguez-Gomez, Diego
2011-01-01
Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find a new invariant under Seiberg duality, namely the Klein j-invariant of the complex structure parameter in the distinguished isoradial embedding of the dimer, determined by the physical R-charges. Additional number theoretic invariants are described in terms of the algebraic number field of the R-charges. We also give a new compact description of the a-maximization procedure by introducing a generalized incidence matrix.
Invariant and semi-invariant probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com
2009-10-15
Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.
On the Galilean non-invariance of classical electromagnetism
International Nuclear Information System (INIS)
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students-and sometimes their teachers too-may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation 'at a glance', on the basis of the presence of a parameter c with the dimensions of a velocity in Maxwell's equations, being well aware of the fact that any velocity is non-invariant in Galilean relativity. This 'obvious' answer, however popular, is not correct due to the actual observer-invariance of the Maxwell parameter c in pre-relativistic physics too. A pre-relativistic physicist would therefore have needed a different explanation. Playing the role of this physicist, we pedagogically show how a proof of the Galilean non-invariance of classical electromagnetism can be obtained, resting on simple pre-relativistic considerations alone
Local Scale Invariance and Inflation
Singh, Naveen K
2016-01-01
We study the inflation and the cosmological perturbations generated during the inflation in a local scale invariant model. The local scale invariant model introduces a vector field $S_{\\mu}$ in this theory. In this paper, for simplicity, we consider the temporal part of the vector field $S_t$. We show that the temporal part is associated with the slow roll parameter of scalar field. Due to local scale invariance, we have a gauge degree of freedom. In a particular gauge, we show that the local scale invariance provides sufficient number of e-foldings for the inflation. Finally, we estimate the power spectrum of scalar perturbation in terms of the parameters of the theory.
Invariant measures for Cherry flows
Saghin, Radu
2011-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we discuss some situations when there exists another invariant measure supported on the quasi-minimal set, which is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Moment Invariants for Object Recognition
Czech Academy of Sciences Publication Activity Database
Flusser, Jan
Boca Raton: Wiley&Sons, 2015. ISBN 9780471346081 Institutional support: RVO:67985556 Keywords : invariants * object recognition * moments Subject RIV: JC - Computer Hardware ; Software http://library.utia.cas.cz/separaty/2015/ZOI/flusser-0442976.pdf
Invariant measures in brain dynamics
International Nuclear Information System (INIS)
This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles
Gauge-invariant approach to quark dynamics
Sazdjian, H.
2016-02-01
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics (QCD) are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green's functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the quark Green's function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large- N c limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
Hiding Lorentz Invariance Violation with MOND
Sanders, R H
2011-01-01
Ho\\v{r}ava gravity is a attempt to construct a renormalizable theory of gravity by breaking the Lorentz Invariance of the gravitational action at high energies. The underlying principle is that Lorentz Invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low energy limit of Ho\\v{r}ava gravity in its non-projectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than $cH_0$; this modification results in the phenomenology of MOND at lower accelerations.
Hiding Lorentz invariance violation with MOND
International Nuclear Information System (INIS)
Horava-Lifshitz gravity is an attempt to construct a renormalizable theory of gravity by breaking the Lorentz invariance of the gravitational action at high energies. The underlying principle is that Lorentz invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low-energy limit of Horava-Lifshitz gravity in its nonprojectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than cH0; this modification results in the phenomenology of modified Newtonian dynamics (MOND) at lower accelerations. As a relativistic theory of MOND, this modified Horava-Lifshitz theory presents several advantages over its predecessors.
Gauge-invariant approach to quark dynamics
Sazdjian, H
2016-01-01
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
Object recognition by implicit invariants
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautsky, J.; Šroubek, Filip
2007-01-01
Roč. 2007, č. 4673 (2007), s. 856-863. ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http:// staff .utia.cas.cz/sroubekf/papers/CAIP_07.pdf
Gauge invariance and lattice monopoles
International Nuclear Information System (INIS)
The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
Classification of Simple Current Invariants
Gato-Rivera, Beatriz
1991-01-01
We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)
Modern Tests of Lorentz Invariance
Directory of Open Access Journals (Sweden)
Mattingly David
2005-09-01
Full Text Available Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
Stability of $(A,\; B)$-invariant subspaces
Puerta Sales, Ferran; Puerta Coll, Xavier
2003-01-01
Given a pair of matrices (A,B) we study the stability of their invariant subspaces from a geometric point of view. The main tool is the manifold of quadruples((A;B); F; S) where S is an (A,B)-invariant subspace and F is such that (A + BF)S C S. From the geometry of this manifold we derive sufficient computable conditions of stability.
Hidden scale invariance of metals
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf R.
2015-11-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W, and Hg), most post-transition metals (Ga, In, Sn, and Tl), and the metalloids Si and Ge cannot be explained by the IPL assumption. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Grüneisen equation of state and a number of well-known empirical melting and freezing rules.
Structure of BRS-invariant local functionals
International Nuclear Information System (INIS)
For a large class of gauge theories a nilpotent BRS-operator s is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of s=s+d on functions f(C,T) of tensor fields T and of variables C which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly cadidates whose BRS-variation vanishes off-shell. The assumptions under which the result holds are thoroughly discussed. (orig.)
Rotation invariant moments and transforms for geometrically invariant image watermarking
Singh, Chandan; Ranade, Sukhjeet K.
2013-01-01
We present invariant image watermarking based on a recently introduced set of polar harmonic transforms and angular radial transforms and their comparative analysis with state-of-art approaches based on Zernike moments and pseudo-Zernike moments (ZMs/PZMs). Similar to ZMs/PZMs, these transforms provide rotation invariance and resilience to noise while mitigating inherent limitations like numerical instability and computational cost at high order of moments. These characteristics motivate us to design invariant transform-based invariant image watermarking schemes that can withstand various intentional or unintentional attacks, handle large bitcarriers, and work in a limited computing environment. A comparative performance evaluation of watermarking systems regarding critical parameters like visual imperceptibility, embedding capacity, and watermark robustness against geometric transformations, common signal processing distortions, and Stirmark attacks is performed along with the empirical analysis of various inherent properties of transforms and moments such as magnitude invariance, reconstruction capabilities, and computational complexity to investigate relationships between the performance of watermarking schemes and inherent properties of transforms.
Local Unitary Invariants for Multipartite Quantum Systems
Wang, Jing; Li, Ming; Fei, Shao-Ming; Li-Jost, Xianqing
2014-01-01
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.
Weyl invariance with a nontrivial mass scale
Alvarez, Enrique
2016-01-01
A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.
Geometric invariance of mass-like asymptotic invariants
Michel, Benoît
2010-01-01
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; but they may be gathered in a divergence, thus having vanishing integral over any closed hypersurface. This fact could only be checked after direct calculation (and was called a...
Second order invariants and holography
Bonanno, Luca; Luongo, Orlando
2011-01-01
Motivated by recent works on the role of the Holographic principle in cosmology, we relate a class of second order Ricci invariants to the IR cutoff characterizing the holographic Dark Energy density. The choice of second order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an \\emph{a priori} assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Trace Invariance for Quaternion Matrices
Directory of Open Access Journals (Sweden)
Ralph John de la Cruz
2015-12-01
Full Text Available Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F such that P is nonsingular, tr A = tr (PAP-1. We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Instanton counting and Donaldson invariants
International Nuclear Information System (INIS)
For a smooth projective toric surface we determine the Donaldson invariants and their wall-crossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture and its refinement , we apply this result to give a generating function for the wall-crossing of Donaldson invariants of good walls of simply connected projective surfaces with b+ = 1 in terms of modular forms. This formula was proved earlier in more generally for simply connected 4-manifolds with b+ = 1, assuming the Kotschick- Morgan conjecture and it was also derived by physical arguments. (author)
Trace Invariance for Quaternion Matrices
Ralph John de la Cruz
2015-01-01
Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F) such that P is nonsingular, tr A = tr (PAP-1). We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Leptogenesis and a Jarlskog Invariant
Davidson, Sacha; Davidson, Sacha; Kitano, Ryuichiro
2004-01-01
The relation between low energy CP violating phases, and the CP asymmetry of leptogenesis, $\\epsilon$, is investigated. Although it is known that in general those are independent, there may be a relation when a model is specified. We construct a Jarlskog invariant which is proportional to $\\epsilon$ if the right-handed neutrino masses are hierarchical. Since the invariant can be expressed in terms of left-handed neutrino parameters--some measurable, and some not--it is useful in identifying the limits in which $\\epsilon$ is related to MNS phases.
Simple Algebras of Invariant Operators
Institute of Scientific and Technical Information of China (English)
Xiaorong Shen; J.D.H. Smith
2001-01-01
Comtrans algebras were introduced in as algebras with two trilinear operators, a commutator [x, y, z] and a translator , which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of hermitian operators over a field with a minimum polynomial x2+1. This paper is about generalizing the hermitian case to the so-called invariant case. The main result of this paper shows that the vector space of n-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.
Singular conformally invariant trilinear forms and generalized Rankin Cohen operators
Jean-Louis, Clerc
2011-01-01
The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\\mathcal C^\\infty_c(\\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin Cohen operators), for which new formul\\ae \\ are obtained. The main tool is a Bernstein-Sato identity for the kernel of the forms.
Xiao, Jing; Bai, Yu; He, Yini; McWhinnie, Chad M.; Ling, Yu; Smith, Hannah; Huebner, E. Scott
2016-01-01
The aim of this study was to test the gender invariance of the Chinese version of the Achievement Goal Questionnaire (AGQ-C) utilizing a sample of 1,115 Chinese university students. Multi-group confirmatory factor analysis supported the configural, metric, and scalar invariance of the AGQ-C across genders. Analyses also revealed that the latent…
Scale-invariant power spectra from a Weyl-invariant scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
Myung, Yun Soo [Inje University, Institute of Basic Sciences and Department of Computer Simulation, Gimhae (Korea, Republic of); Park, Young-Jai [Sogang University, Department of Physics, Seoul (Korea, Republic of)
2016-02-15
We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar-tensor theory in de Sitter spacetime. This implies that the Weyl invariance guarantees the implementation of the scale invariance of the power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl invariance of the action and the scale invariance of the power spectrum in de Sitter spacetime. (orig.)
Donaldson invariants of symplectic manifolds
Sivek, Steven
2013-01-01
We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the sphere which evaluate maximally on a generic fiber.
Identity from classical invariant theory
International Nuclear Information System (INIS)
A simple derivation is given of a well-known relation involving the so-called Cayley Operator of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics
Supersymmetric gauge invariant interaction revisited
International Nuclear Information System (INIS)
A supersymmetric Lagrangian invariant under local U(1) gauge transformations is written in terms of a non-chiral superfield which substitute the usual vector supermultiplet together with chiral and anti-chiral superfields. The Euler equations allow us to obtain the off-shell version of the usual Lagrangian for supersymmetric quantum-electrodynamics (SQED). (Author)
Geng, C. Q.; Geng, Lei
2005-01-01
We first briefly review tests on CPT invariance based on the consequences of the CPT theorem and then present some possible CPT tests due to exotic models in which some of the CPT conditions are lost, such as those without hermiticity.
Translation-invariant noncommutative renormalization
Tanasa, Adrian
2010-01-01
We review here the construction of a translation-invariant scalar model which was proved to be renormalizable on Moyal space. Some general considerations on non-local renormalizability are given. Finally, we present perspectives for generalizing these quantum field theoretical techniques to group field theory, a new setting for quantum gravity.
Lorentz invariance and gauge equivariance
International Nuclear Information System (INIS)
Trying to place Lorentz and gauge transformations on the same foundation, it turns out that the first one generates invariance, the second one equivariance, at least for the abelian case. This similarity is not a hypothesis but is supported by and a consequence of the path integral formalism in quantum field theory.
Invariants in Supersymmetric Classical Mechanics
Alonso Izquierdo, Alberto; González León, Miguel Ángel; Mateos Guilarte, Juan
2000-01-01
[EN] The bosonic second invariant of SuperLiouville models in supersymmetric classical mechanics is described. [ES] El segundo campo cuántico de bosones invariante del modelo SuperLiouville es descrito en la mecanica clasica supersimétrica.
Invariant Classification of Gait Types
DEFF Research Database (Denmark)
Fihl, Preben; Moeslund, Thomas B.
2008-01-01
This paper presents a method of classifying human gait in an invariant manner based on silhouette comparison. A database of artificially generated silhouettes is created representing the three main types of gait, i.e. walking, jogging, and running. Silhouettes generated from different camera angles...
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
Hjorth, Poul G.
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon in...
Conjectured enumeration of Vassiliev invariants
Broadhurst, D J
1997-01-01
These conjectures are motivated by successful enumerations of irreducible Euler sums. Predictions for $\\beta_{15,10}$, $\\beta_{16,12}$ and $\\beta_{19,16}$ suggest that the action of sl and osp Lie algebras, on baguette diagrams with ladder insertions, fails to detect an invariant in each case.
Scale invariance and superfluid turbulence
Energy Technology Data Exchange (ETDEWEB)
Sen, Siddhartha, E-mail: siddhartha.sen@tcd.ie [CRANN, Trinity College Dublin, Dublin 2 (Ireland); R.K. Mission Vivekananda University, Belur 711 202, West Bengal (India); Ray, Koushik, E-mail: koushik@iacs.res.in [Department of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta 700 032 (India)
2013-11-11
We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot–Savart interaction between the observed filament excitations of the system as well.
Pairing interaction and Galilei invariance
International Nuclear Information System (INIS)
The relation between Galilei invariance and the energy weighted sum rule for a mass dipole operator is discussed using a monopole pairing interaction. It is found that the energy weighted sum rule for the mass dipole operator changes as much as 18% in medium and heavy nuclei. copyright 1997 The American Physical Society
Test of Lorentz Invarience from Compton Scattering
Mohanmurthy, Prajwal; Narayan, Amrendra
2015-01-01
In the recent times, test of Lorentz Invariance has been used as a means to probe theories of physics beyond the standard model, especially those such as extensions to String Theory and Quantum Gravity. Tests of Lorentz invariance could go a long way in setting the stage for possible quantum gravity theories which are beyond the standard model. We describe a simple way of utilizing the polarimeters, which are a critical beam instrument at precision and intensity frontier nuclear physics labs such as Stanford Linear Accelerator Center (SLAC) and Jefferson Lab (JLab), to limit the dependence of speed of light with the energy of the photons. Furthermore, we also describe a way of limiting directional dependence of speed of light at previously unprecedented levels of precision by studying the sidereal variations. We obtain a limit of MSME parameters: $\\sqrt{\\kappa_X^2 + \\kappa_Y^2} < 2.4 \\times 10^{-17}$ and $\\sqrt{\\left( 2c_{TX} - (\\tilde{\\kappa}_{0^+}^{YZ} \\right)^2 + \\left( 2c_{TY} - (\\tilde{\\kappa}_{0^+}^{...
Gauge-invariant cosmological density perturbations
International Nuclear Information System (INIS)
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
Baryogenesis in a CP invariant theory
Hook, Anson
2015-01-01
We consider baryogenesis in a model which has a CP invariant Lagrangian, CP invariant initial conditions and does not spontaneously break CP at any of the minima. We utilize the fact that tunneling processes between CP invariant minima can break CP to implement baryogenesis. CP invariance requires the presence of two tunneling processes with opposite CP breaking phases and equal probability of occurring. In order for the entire visible universe to see the same CP violating phase, we consider ...
Energy balance invariance for interacting particle systems
Yavari, Arash; Marsden, Jerrold E.
2009-01-01
This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However, the postulate of invariance of balance of ener...
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....
On Link Invariants and Topological String Amplitudes
Ramadevi, P; Sarkar, Tapobrata
2001-01-01
We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. From the multi-component link invariants in SU(N) Chern-Simons theory, we suggest a form for the new polynomial invariants.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Geometry-Invariant Resonant Cavities
Liberal, Iñigo; Engheta, Nader
2015-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional cavities are a function of its geometry, and, thus, the size and shape of a resonant cavity is selected in order to operate at a specific frequency. Here, we demonstrate theoretically the existence of geometry-invariant resonant cavities, i.e., resonators whose eigenfrequency is invariant with respect to geometrical deformations. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, which enable decoupling of the time and spatial field variations. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.
Gauge invariance and holographic renormalization
Directory of Open Access Journals (Sweden)
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Relativistically invariant photonic wave packets
Bradler, Kamil
2009-01-01
We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.
Anisotropic invariance in minisuperspace models
Chagoya, Javier; Sabido, Miguel
2016-06-01
In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski–Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann–Robertson–Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.
Blur Invariants and Projection Operators
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Suk, Tomáš; Boldyš, Jiří; Zitová, Barbara
Indbruck: ACTA Press, 2013 - (Linsen, L.; Kampel, M.), s. 305-312. (Computer Graphics and Imaging. 798). ISBN 978-0-88986-944-8. [Signal Processing , Pattern Recognition and Applications (SPPRA 2013). Insbruck (AT), 12.02.2013-14.02.2013] R&D Projects: GA ČR GAP103/11/1552 Keywords : image recognition * Fourier transform * projection operators * invariants Subject RIV: JD - Computer Applications, Robotics
A reparametrization invariant surface ordering
Gustavsson, Andreas
2005-01-01
We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.
Gauge Invariance in Classical Electrodynamics
Engelhardt, W
2005-01-01
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uniqueness is not justified. The reason for this failure is traced back to the inhomogeneous wave equations which connect the propagating fields and their sources at the same time.
Learning Local Invariant Mahalanobis Distances
Fetaya, Ethan; Ullman, Shimon
2015-01-01
For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a loca...
SCALe-invariant Integral Surfaces
Zanni, C.; A. Bernhardt; Quiblier, M.; Cani, M.-P.
2013-01-01
Extraction of skeletons from solid shapes has attracted quite a lot of attention, but less attention was paid so far to the reverse operation: generating smooth surfaces from skeletons and local radius information. Convolution surfaces, i.e. implicit surfaces generated by integrating a smoothing kernel along a skeleton, were developed to do so. However, they failed to reconstruct prescribed radii and were unable to model large shapes with fine details. This work introduces SCALe-invariant Int...
Conformal Invariance of Graphene Sheets
Giordanelli, I.; Posé, N.; Mendoza, M.; Herrmann, H. J.
2016-01-01
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces. PMID:26961723
Finite type invariants and fatgraphs
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry;
2010-01-01
the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an......We define an invariant G(M) of pairs M,G , where M is a 3-manifold obtained by surgery on some framed link in the cylinder Σ×I , Σ is a connected surface with at least one boundary component, and G is a fatgraph spine of Σ. In effect, G is the composition with the ιn maps of Le–Murakami–Ohtsuki of...... isomorphism from an appropriate vector space of homology cylinders to a certain algebra of Jacobi diagrams. Via composition for any pair of fatgraph spines G,G′ of Σ, we derive a representation of the Ptolemy groupoid, i.e., the combinatorial model for the fundamental path groupoid of Teichmüller space, as a...
Institute of Scientific and Technical Information of China (English)
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2005-01-01
This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.
Scale vs Conformal invariance from Entanglement Entropy
Naseh, Ali
2016-01-01
For a generic conformal field theory (CFT) in four dimensions, the scale anomaly dictates that the universal part of entanglement entropy across a sphere ($\\mathcal{C}_{\\text{univ}}(S^{2})$) is positive. Based on this fact, we explore the consequences of assuming positive sign for $\\mathcal{C}_{\\text{univ}}(S^{2})$ in a four dimensional scale invariant theory (SFT). In absence of a dimension two scalar operator $\\mathcal{O}_{2}$ in the spectrum of a SFT, we show that this assumption suggests that SFT is a CFT. In presence of $\\mathcal{O}_{2}$, we show that this assumption can fix the coefficient of the nonlinear coupling term $\\int\\hspace{-.5mm} d^{4}x\\sqrt{g} R\\mathcal{O}_{2}$ to a conformal value.
Quantum moment maps and invariants for G-invariant star products
Hamachi, Kentaro
2002-01-01
We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star pro...
Quasi-Invariants of Complex Reflection Groups
Berest, Yuri
2009-01-01
We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the coordinate ring of some (singular) affine variety X_k. We extend the main results of Etingof, Ginzburg and the first author (see [BEG]) to this setting: in particular, we show that the variety X_k and the module Q_k are Cohen-Macaulay, and the rings of differential operators on X_k and Q_k are simple rings, Morita equivalent to the Weyl algebra A_n(C), where n = dim X_k . Our approach relies on representation theory of complex Cherednik algebras and is parallel to that of [BEG]. As a by-product, we prove the existence of shift operators for an arbitrary complex reflection group, confirming a conjecture of Dunkl and Opdam. Another result is a proof of a conjecture of Opdam, concerning certain operations (KZ twists) on the set of irreducible representations of W.
Shape-Invariant Fuzzy Clustering of Proteomics Data
Berthold, Michael R; Patterson, David E.; Ortolani, Marco; Hofer, Heiko; Höppner, Frank; Callan, Ondine
2002-01-01
In this paper we present a variant of fuzzy c-means that allows to find similar shapes in time series data in a scale-invariant fashion. We use data from protein mass spectrography to show how this approach finds areas of interest without a need for ad-hoc normalizations.
Invariant coefficients of diffusion in iron-chromium-nickel system
Energy Technology Data Exchange (ETDEWEB)
Mokrov, A.P.; Akimov, V.K.; Golubev, V.G.
1984-02-01
The temperature and concentration dependences of the Dsub(c) coefficients in the ..gamma..-phase of iron-chromium-nickel system are determined. It is proposed to described mutual diffusion in multicomponent systems using invariant, i.e. independent of the choice of solvent, coefficients of diffusion. The assumption that their temperature dependence follows the Arrhenius law is confirmed by the experiment.
Invariant coefficients of diffusion in iron-chromium-nickel system
International Nuclear Information System (INIS)
The temperature and concentration dependences of the Dsub(c) coefficients in the γ-phase of iron-chromium-nickel system are determined. It is proposed to described mutual diffusion in mul-- ticomponent systems using invariant, i. e. independent of the choice of solvent, coefficients of diffusion. The assumption that their temperature dependence follows the Arrhenius law is confirmed by the experiment
Electromagnetic interaction in theory with Lorentz invariant CPT violation
Energy Technology Data Exchange (ETDEWEB)
Chaichian, Masud, E-mail: Masud.Chaichian@helsinki.fi [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland); Fujikawa, Kazuo [Mathematical Physics Laboratory, RIKEN Nishina Center, Wako 351-0198 (Japan); Tureanu, Anca [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland)
2013-01-29
An attempt is made to incorporate the electromagnetic interaction in a Lorentz invariant but CPT violating non-local model with particle-antiparticle mass splitting, which is regarded as a modified QED. The gauge invariance is maintained by the Schwinger non-integrable phase factor but the electromagnetic interaction breaks C, CP and CPT symmetries. Implications of the present CPT breaking scheme on the electromagnetic transitions and particle-antiparticle pair creation are discussed. The CPT violation such as the one suggested in this Letter may open a new path to the analysis of baryon asymmetry since some of the Sakharov constraints are expected to be modified.
Volume conjecture for $SU(n)$-invariants
Chen, Qingtao; Zhu, Shengmao
2015-01-01
This paper discuss an intrinsic relation among congruent relations \\cite{CLPZ}, cyclotomic expansion and Volume Conjecture for $SU(n)$ invariants. Motivated by the congruent relations for $SU(n)$ invariants obtained in our previous work \\cite{CLPZ}, we study certain limits of the $SU(n)$ invariants at various roots of unit. First, we prove a new symmetry property for the $SU(n)$ invariants by using a symmetry of colored HOMFLYPT invariants. Then we propose some conjectural formulas including the cyclotomic expansion conjecture and volume conjecture for $SU(n)$ invariants (specialization of colored HOMFLYPT invariants). We also give the proofs of these conjectural formulas for the case of figure-eight knot.
Role of gauge invariance in B -> V gamma radiative weak decays
Riazuddin, M
2002-01-01
The role of gauge invariance in calculating B -> V gamma radiative weak decays is clarified. It is shown that the gauge invariance severely restricts the contributions mediated by the usual weak non-leptonic Hamiltonian dominated by u and c quaks with one photon attachment. Such contributions are found to be almost negligible.
Scale invariance and renormalization group
International Nuclear Information System (INIS)
Scale invariance enabled the understanding of cooperative phenomena and the study of elementary interactions, such as phase transition phenomena, the Curie critical temperature and spin rearrangement in crystals. The renormalization group method, due to K. Wilson in 1971, allowed for the study of collective phenomena, using an iterative process from smaller scales to larger scales, leading to universal properties and the description of matter state transitions or long polymer behaviour; it also enabled to reconsider the quantum electrodynamic theory and its relations to time and distance scales
Invariants of quadratic differential forms
Wright, Joseph Edmund
2013-01-01
This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. Suitable for advanced undergraduates and graduate students of mathematics, it avoids unnecessary analysis and offers an accessible view of the field for readers unfamiliar with the subject.A historical overview is followed by considerations of the methods of Christoffel and Lie as well as Maschke's symbolic method and explorations of geometrical and dynamical methods. The final chapter on applications, which d
Quantum Weyl invariance and cosmology
Dabholkar, Atish
2016-09-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Quantum Weyl Invariance and Cosmology
Dabholkar, Atish
2015-01-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Tensor network methods for invariant theory
International Nuclear Information System (INIS)
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state (MPS) factorization) when studying polynomial invariants. As our main example, we consider invariants of MPSs. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the Rényi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as MPSs, contain excellent tools that can be applied in the study of invariants. (paper)
Entangling power of permutation-invariant quantum states
International Nuclear Information System (INIS)
We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of n sites in a system of length L generically grows as σ log2[2πen(L-n)/L]+C, where σ is the on-site spin and C is a function depending only on magnetization
Equivalent topological invariants of topological insulators
Energy Technology Data Exchange (ETDEWEB)
Wang Zhong [Department of Modern Physics, University of Science and Technology of China, Hefei, 230026 (China); Qi Xiaoliang; Zhang Shoucheng, E-mail: sczhang@stanford.ed [Department of Physics, Stanford University, Stanford, CA 94305 (United States)
2010-06-15
A time-reversal (TR) invariant topological insulator can be generally defined by the effective topological field theory with a quantized {theta} coefficient, which can only take values of 0 or {pi}. This theory is generally valid for an arbitrarily interacting system and the quantization of the {theta} invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the {theta} invariant can be expressed as an integral over the entire three-dimensional Brillouin zone. Alternatively, non-interacting insulators can be classified by topological invariants defined over discrete TR invariant momenta. In this paper, we show the complete equivalence between the integral and the discrete invariants of the topological insulator.
Equivalent topological invariants of topological insulators
Wang, Zhong; Qi, Xiao-Liang; Zhang, Shou-Cheng
2009-01-01
A time-reversal invariant topological insulator can be generally defined by the effective topological field theory with a quantized \\theta coefficient, which can only take values of 0 or \\pi. This theory is generally valid for an arbitrarily interacting system and the quantization of the \\theta invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the \\theta invariant can be expressed as an integral over the entire three dimensional Brillouin zone...
Knot invariants and higher representation theory
Webster, Ben
2013-01-01
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel and Sussan for sl_n. Our technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimens...
Light Speed Invariance is a Remarkable Illusion
Gift, Stephan J. G.
2007-01-01
Though many experiments appear to have confirmed the light speed invariance postulate of special relativity theory, this postulate is actually unverified. This paper resolves this issue by first showing the manner in which an illusion of light speed invariance occurs in two-way light speed measurement in the framework of a semi-classical absolute space theory. It then demonstrates a measurable variation of the one-way speed of light, which directly invalidates the invariance postulate and con...
On factorization invariants and Hilbert functions
O'Neill, Christopher
2015-01-01
Nonunique factorization in commutative semigroups is often studied using factorization invariants, which assign to each semigroup element a quantity determined by the factorization structure. For numerical semigroups (additive subsemigroups of the natural numbers), several factorization invariants are known to admit predictable behavior for sufficiently large semigroup elements. In particular, the catenary degree and delta set invariants are both eventually periodic, and the omega-primality i...
Wilson loop invariants from WN conformal blocks
Alekseev, Oleg; Novaes, Fábio
2015-12-01
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU (N), which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
Baryogenesis in a CP invariant theory
Hook, Anson
2015-01-01
We consider baryogenesis in a model which has a CP invariant Lagrangian, CP invariant initial conditions and does not spontaneously break CP at any of the minima. We utilize the fact that tunneling processes between CP invariant minima can break CP to implement baryogenesis. CP invariance requires the presence of two tunneling processes with opposite CP breaking phases and equal probability of occurring. In order for the entire visible universe to see the same CP violating phase, we consider a model where the field doing the tunneling is the inflaton.
Wilson loop invariants from WN conformal blocks
Directory of Open Access Journals (Sweden)
Oleg Alekseev
2015-12-01
Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
Conformal invariance conserved quantity of Hamilton systems
Institute of Scientific and Technical Information of China (English)
Cai Jian-Le; Luo Shao-Kai; Mei Feng-Xiang
2008-01-01
This paper studies conformal invariance and comserved quantRies of Hamilton system.The definition and the determining equation of conformal invariance for Hamilton system are provided.The relationship between the conformal invariance and the Lie symmetry are discussed,and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced.It gives the conserved quantities of the system and an example for illustration.
Optimized Set of RST Moment Invariants
Directory of Open Access Journals (Sweden)
Khalid M. Hosny
2008-01-01
Full Text Available Moment invariants are widely used in image processing, pattern recognition and computer vision. Several methods and algorithms have been proposed for fast and efficient calculation of moment's invariants where numerical approximation errors are involved in most of these methods. In this paper, an optimized set of moment invariants with respect to rotation, scaling and translation is presented. An accurate method is used for exact computation of moment invariants for gray level images. A fast algorithm is applied to accelerate the process of computation. Error analysis is presented and a comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Introduction to Vassiliev Knot Invariants
Chmutov, S; Mostovoy, J
2011-01-01
This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and as a guide to some of the more advanced material. Our aim is to lead the reader to understanding by means of pictures and calculations, and for this reason we often prefer to convey the idea of the proof on an instructive example rather than give a complete argument. While we have made an effort to make the text reasonably self-contained, an advanced reader is sometimes referred to the original papers for the technical details of the proofs.
Cardinal invariants on Boolean algebras
Monk, J Donald
2014-01-01
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...
Uniform distribution of Hasse invariants
Directory of Open Access Journals (Sweden)
R. A. Mollin
1985-03-01
Full Text Available I. Schur's study of simple algebras around the turn of the century, and subsequent investigations by R. Brauer, E. Witt and others, were later reformulated in terms of what is now called the Schur subgroup of the Brauer group. During the last twenty years this group has generated substantial interest and numerous palatable results have ensued. Among these is the discovery that elements of the Schur group satisfy uniform distribution of Hasse invariants. It is the purpose of this paper to continue an investigation of the latter concept and to highlight certain applications of these results, not only to the Schur group, but also to embeddings of simple algebras and extensions of automorphisms, among others.
Pattern Recognition by Combined Invariants
Institute of Scientific and Technical Information of China (English)
WANG Xiaohong; ZHAO Rongchun
2001-01-01
A feature-based recognition of objectsor patterns independent of their position, size, orien-tation and other variations has been the goal of muchrecent research. The existing approaches to invarianttwo-dimensional pattern recognition are useless whenpattern is blurred. In this paper, we present a novelpattern recognition system which can solve the prob-lem by using combined invariants as image features.The classification technique we choose for our systemis weighted normalized cross correlation. The mean ofthe intraclass standard deviations of the kth featureover the total number of prototypes for each class isused as a weighting factor during the classification pro-cess to improve recognition accuracy. The feasibilityof our pattern recognition system and the invarianceof the combined features with respect to translation,scaling, rotation and blurring are approved by numer-ical experiments on head images.
Dynamical invariance for random matrices
Unterberger, Jeremie
2016-01-01
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\"odinger-Virasoro algebra.
Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products
Costello, Kevin
2003-01-01
I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S^{g+1}(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.
Invariant sets near singularities of holomorphic foliations
Camacho, César; Rosas, Rudy
2013-01-01
Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\\mathcal{I}$ contains either a separatrix at $p$ or an invariant real three dimensional manifold singular at $p$.
Uniqueness in ergodic decomposition of invariant probabilities
Zimmermann, Dieter
1992-01-01
We show that for any set of transition probabilities on a common measurable space and any invariant probability, there is at most one representing measure on the set of extremal, invariant probabilities with the $\\sigma$-algebra generated by the evaluations. The proof uses nonstandard analysis.
A rephasing invariant study of neutrino mixing
Chiu, S H
2015-01-01
We derive a set of renormalization group equations (RGE) for Dirac neutrinos using a rephasing invariant parametrization. The symmetric properties of these equations under flavor permutation facilitate the derivation of some exact and approximate RGE invariants. Even though the complete analytical solutions for the RGE are unavailable, we provide a numerical example that illustrate the evolution of the neutrino mixing parameters.
Spectral properties of supersymmetric shape invariant potentials
Indian Academy of Sciences (India)
Barnali Chakrabarti
2008-01-01
We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.
Borromean surgery formula for the Casson invariant
DEFF Research Database (Denmark)
Meilhan, Jean-Baptiste Odet Thierry
2008-01-01
It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing...
Synthesizing Chaotic Maps with Prescribed Invariant Densities
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2004-01-01
The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.
Polynomial Invariant Theory of the Classical Groups
Westrich, Quinton
2011-01-01
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \\emph{basic invariants}. In particular, we set out to find the set of basic invariants for the classical groups GL$(V)$, O$(n)$, and Sp$(n)$ for $n$ even. In the first half of the paper we set up relevant definitions and theorems for our search for the set of basic invariants, starting with linear algebraic groups and then discussing associative algebras. We then state and prove a monumental theorem that will allow us to proceed with hope: it says that the set of basic invariants is finite if $G$ is reductive. Finally we state without proof the First Fundamental Theorems, which aim to list explicitly the relevant sets of basic invariants, for the classical groups above. We end by commenting on some applications of invariant theory, on the history of its development, and stating a useful theorem in the appendix whose proof lies beyond the scope ...
Transverse invariant higher-spin fields
Energy Technology Data Exchange (ETDEWEB)
Skvortsov, E.D. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, 119991 Moscow (Russian Federation)], E-mail: eugene.skvortsov@gmail.com; Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, 119991 Moscow (Russian Federation)], E-mail: vasiliev@lpi.ru
2008-06-26
It is shown that a symmetric massless bosonic higher-spin field can be described by a traceless tensor field with reduced (transverse) gauge invariance. The Hamiltonian analysis of the transverse gauge invariant higher-spin models is used to control a number of degrees of freedom.
Stability of (A,B)-invariant subspaces
Peña Carrera, Marta; Puerta Coll, Xavier; Puerta Sales, Ferran
2005-01-01
Given a pair of matrices (A;B) we study the stability of their invariant subspaces from the geometry of the manifold of quadruples (A;B; S; F) where S is an (A;B)-invariant subspace and F is such that (A + BF)S ½ S. In particular, we derive a su±cient computable condition of stability.
Rational Invariants of the Generalized Classical Groups
Institute of Scientific and Technical Information of China (English)
NAN JI-ZHU; ZHAO JING
2011-01-01
In this paper, we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B, N and T, and we also compute the orders of them. Furthermore, we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group.
Scale invariant Volkov–Akulov supergravity
Directory of Open Access Journals (Sweden)
S. Ferrara
2015-10-01
Full Text Available A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
1-Loop Matching of gauge invariant dim-6 operators for B decays
Aebischer, Jason; Fael, Matteo; Greub, Christoph
2016-01-01
Physics beyond the Standard Model, realized above the electroweak scale, can be incorporated in a model independent way in the Wilson coefficients of higher dimensional gauge invariant operators. In these proceedings we review the matching of the $SU(3)_C\\times SU(2)_L\\times U(1)_Y$ gauge invariant dimension-six operators on the effective Hamiltonian governing $b\\to s$ and $b\\to c$ transitions, including the leading 1-loop effects.
Constructing Invariant Fairness Measures for Surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
1998-01-01
This paper presents a general method which from an invariant curve fairness measure constructs an invariant surface fairness measure. Besides the curve fairness measure one only needs a class of curves on the surface for which one wants to apply the curve measure. The surface measure at a point is...... variation.The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Such a family is generated by the flow of a vector field, orthogonal to the curves. The first, respectively the second order derivative along the curve of...... the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together with...
Geometric invariance of compressible turbulent boundary layers
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Construction and Fourier analysis of invariant surfaces from tracking data
International Nuclear Information System (INIS)
We study invariant surfaces in phase space by application of a symplectic tracking code. For motion in two degrees of freedom we use the code to compute I(s), /Phi/(s) for s = 0,C,2C...nC, where I = (I1,I2), /Phi/ = (/phi/1,/phi/2) are action-angle coordinates of points on a single orbit, and C is the circumference of the reference orbit. As a test to see whether the orbit lies on an invariant surface (i.e., to test for regular and nonresonant motion) we fit the points to a smooth, piece-wise polynomial surface I = /cflx I/(/phi/1,/phi/2). We then compute additional points on the same orbit, and test for their closeness to /cflx I/. We find that data from a few thousand turns are sufficient to construct accurate approximations to an invariant surface, even in cases with strong nonlinearities. Two-dimensional Fourier analysis of the surface leads to information on the strength of nonlinear resonances, and provides the generator of a canonical transformation as a Fourier series in angle variables. The generator can be used in a program to derive rigorous bounds on the motion for a finite time T. 6 refs., 2 figs., 1 tab
Magnetic monopoles, Galilean invariance, and Maxwell's equations
Crawford, Frank S.
1992-02-01
Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, ``as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant-i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v<<c are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula.
Magnetic monopoles, Galilean invariance, and Maxwell's equations
International Nuclear Information System (INIS)
Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, ''as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v much-lt c are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula
Is the speed of light invariant or covariant?
Sasso, Daniele
2010-01-01
According to the theory of ether light propagates with constant speed c with respect to the absolute reference frame and with respect to any other reference frame the speed of light is covariant. According to the theory of special relativity the speed of light is invariant with respect to any reference frame. The new theory of reference frames gives a different answer to this question with the consideration of two speeds of light: the physical speed and the relativistic speed. After consideri...
Conformal invariant two particle processes
International Nuclear Information System (INIS)
For the conformal group (essentially the SO2(n,2)group) in n-dimensional Minkowsi-space homogeneous spaces are studied which can be interpreted as 2-particle configuration spaces, and 2-particle representations are induced (both participants are spin 0 particles). The eigensolutions of the Casimir-operator in momentum space are Clebsch-Gordan coefficients in momentum basis. The separation of a complete set of comuting operators from the Casimir eigenvalue equations results in all cases in differential equations with 2 variables (a direct consequence of the rank 2 of the homogen spaces), which can be classified as 'generalized hypergeometric differential operators in 2 variables' (this type, as the author supposes, has not been delt with in the literature so far). In the second part the classical conform invariant (relativistic) 2-particle problem, corresponding to the common quantum mechanical (or quantum field theoretical) problem, is presented and solved completely. It is shown for example that for participant momentums (reasonable in the classic sens) on the forward - or on the zero cone only scattering and no bound states are found. (orig./WBU)
On solvable lattice models and knot invariants
Gepner, D
1993-01-01
Recently, a class of solvable interaction round the face lattice models (IRF) were constructed for an arbitrary rational conformal field theory (RCFT) and an arbitrary field in it. The Boltzmann weights of the lattice models are related in the extreme ultra violet limit to the braiding matrices of the rational conformal field theory. In this note we use these new lattice models to construct a link invariant for any such pair of an RCFT and a field in it. Using the properties of RCFT and the IRF lattice models, we prove that the invariants so constructed always obey the Markov properties, and thus are true link invariants. Further, all the known link invariants, such as the Jones, HOMFLY and Kauffman polynomials arise in this way, along with giving a host of new invariants, and thus also a unified approach to link polynomials. It is speculated that all link invariants arise from some RCFT, and thus the problem of classifying link and knot invariants is equivalent to that of classifying two dimensional conforma...
Feedback-Driven Dynamic Invariant Discovery
Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz
2014-01-01
Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.
A scale invariance criterion for LES parametrizations
Directory of Open Access Journals (Sweden)
Urs Schaefer-Rolffs
2015-01-01
Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.
Gromov-Witten invariants and localization
Morrison, David R
2016-01-01
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold. We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.
On Metrizability of Invariant Affine Connections
Tanaka, Erico
2011-01-01
The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection of a G-invariant metric field. In this paper we analyze the G-metrizability equations for the rotation group G = SO(3), acting canonically on three- and four-dimensional Euclidean spaces. We show that the property of the connection to be SO(3)-invariant allows us to find complete explicit description of all solutions of the SO(3)-metrizability equations.
Invariants of the local Clifford group
International Nuclear Information System (INIS)
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Clifford operators in terms of linear operations over GF(2). Such a study of polynomial invariants of the local Clifford group is mainly of importance in quantum coding theory, in particular in the classification of binary quantum codes. Some applications in entanglement theory and quantum computing are briefly discussed as well
Comment on ``Pairing interaction and Galilei invariance''
Arias, J. M.; Gallardo, M.; Gómez-Camacho, J.
1999-05-01
A recent article by Dussel, Sofia, and Tonina studies the relation between Galilei invariance and dipole energy weighted sum rule (EWSR). The authors find that the pairing interaction, which is neither Galilei nor Lorentz invariant, produces big changes in the EWSR and in effective masses of the nucleons. They argue that these effects of the pairing force could be realistic. In this Comment we stress the validity of Galilei invariance to a very good approximation in this context of low-energy nuclear physics and show that the effective masses and the observed change in the EWSR for the electric dipole operator relative to its classical value are compatible with this symmetry.
On invariant measures of nonlinear Markov processes
Directory of Open Access Journals (Sweden)
N. U. Ahmed
1993-01-01
Full Text Available We consider a nonlinear (in the sense of McKean Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.
Local and gauge invariant observables in gravity
Khavkine, Igor
2015-01-01
It is well known that General Relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price, that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants, gives a general scheme for...
Invariant Spectral Hashing of Image Saliency Graph
Taquet, Maxime; De Vleeschouwer, Christophe; Macq, Benoit
2010-01-01
Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image. The gist of our approach relies on the geometric characterization of salient point distribution in the image. This is achieved by the definition of a "saliency graph" connecting these points jointly with an image intensity function on the graph nodes. An invariant hash is then obtained by considering the spectrum of this function in the eigenvector basis of the Laplacian graph, that is, its graph Fourier transform. Interestingly, this spectrum is invariant under any relabeling of the graph nodes. The graph reveals geomet...
Kinematical bound in asymptotically translationally invariant spacetimes
Shiromizu, T; Tomizawa, S; Shiromizu, Tetsuya; Ida, Daisuke; Tomizawa, Shinya
2004-01-01
We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.
Invariant Solutions for Soil Water Equations
Baikov, V.; Khalique, C.
1999-01-01
We obtain exact solutions for a class of nonlinear partial differential equations which models soil water infiltration and redistribution in a bedded soil profile irrigated by a drip irrigation system. The solutions obtained are invariant under two parameter symmetry groups.
Fourier tranform in exponential rearrangement invariant spaces
Ostrovsky, E.; Sirota, L.
2004-01-01
In this article we investigate the Fourier series and transforms for the functions defined on the $ [0, 2 \\pi]^ d $ or $ R^d $ and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.
On link invariants and topological string amplitudes
International Nuclear Information System (INIS)
We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold
The holonomy expansion: Invariants and approximate supersymmetry
International Nuclear Information System (INIS)
In this paper we give a new expansion, based on cyclicity of the trace, to study regularity properties of twisted expectations =TrH(γU(θ)X(s)). Here X(s)=X0e-s0Q2X1e-s1Q2...Xke-skQ2 is a product of operators Xj, regularized by heat kernels e-sjQ2 with sj>0. The twist groups γ(set-membership sign)Z2 and U(θ)(set-membership sign)U(1) are commuting symmetries of Q2. The name ''holonomy expansion'' arises from picturing as a circular graph, with vertices in the graph representing the operators Xj, in the order that they appear in the product, and the line-segment following Xj representing the heat kernel e-sjQ2. The trace functional is cyclic, so the graph is circular. We generate our expansion by ''transporting'' a vertex Xk around the circle, ending in its original position. We choose an Xk that transforms under a one-dimensional representation of Z2xU(1). For θ in the complement of the discrete set γsing (where the group Z2xU(1) acts trivially on Xk) we obtain an identity between the original expectation and some new expectations. We study an example from supersymmetric quantum mechanics, with a Dirac operator Q(λ) depending on a parameter λ and with a U(1) group of symmetries U(θ). We apply our expansion to invariants Z(λ;θ)=Z(Q(λ);θ) suggested by non-commutative geometry. These invariants are sums of expectations of the form above. We investigate this example as a first step toward developing an expansion to evaluate related invariants arising in supersymmetric quantum field theory. We establish differentiability of Z(λ; θ) in λ for λ(set-membership sign)(0,1] and show Z(λ; θ) is independent of λ. We wish to evaluate Z(λ; θ) at the endpoint λ=0, but Z(0; θ) is ill-defined. We regularize the endpoint, while preserving the U(θ)-symmetry, by replacing Q(λ)2 with H(ε,λ)=Q(λ)2+ε2|z|2. The regularized function Z(ε, λ; θ) depends on all three variables ε, λ, θ; for fixed θ, it is differentiable in the unit (ε, λ) square, except at
Symmetry, Invariance and Ontology in Physics and Statistics
Directory of Open Access Journals (Sweden)
Julio Michael Stern
2011-09-01
Full Text Available This paper has three main objectives: (a Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics or subjective (in statistics interpretations vs. objective interpretations that are suggested by symmetry and invariance arguments; (c Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion.
Conformal Invariance in Classical Field Theory
Grigore, D. R.
1993-01-01
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.
Gauge Invariant Monopoles in SU(2) Gluodynamics
Gubarev, F V
2002-01-01
We introduce a gauge invariant topological definition of monopole charge in pure SU(2) gluodynamics. The non-trivial topology is provided by hedgehog configurations of the non-Abelian field strength tensor on the two-sphere surrounding the monopole. It is shown that this definition can be formulated entirely in terms of Wilson loops which makes the gauge invariance manifest. Moreover, it counts correctly the monopole charge in case of spontaneously broken gauge symmetry and of pure Abelian gauge fields.
Conformal Invariance of Black Hole Temperature
Jacobson, Ted; Kang, Gungwon
1993-01-01
It is shown that the surface gravity and temperature of a stationary black hole are invariant under conformal transformations of the metric that are the identity at infinity. More precisely, we find a conformal invariant definition of the surface gravity of a conformal Killing horizon that agrees with the usual definition(s) for a true Killing horizon and is proportional to the temperature as defined by Hawking radiation. This result is reconciled with the intimate relation between the trace ...
A Homeomorphism Invariant for Substitution Tiling Spaces
Ormes, Nic; Radin, Charles; Sadun, Lorenzo
2000-01-01
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Cech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as ...
Invariant and type inference for matrices
Henzinger, Thomas A.; Hottelier, Thibaud; Kovács, Laura; Voronkov, Andrei
2010-01-01
Wepresentalooppropertygenerationmethodforloopsiteratingover multi-dimensional arrays. When used on matrices, our method is able to infer their shapes (also called types), such as upper-triangular, diagonal, etc. To gen- erate loop properties, we first transform a nested loop iterating over a multi- dimensional array into an equivalent collection of unnested loops. Then, we in- fer quantified loop invariants for each unnested loop using a generalization of a recurrence-based invariant generati...
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Invariants of Fokker-Planck equations
Abe, Sumiyoshi
2016-01-01
A weak invariant of a stochastic system is defined in such a way that its expectation value with respect to the distribution function as a solution of the associated Fokker-Planck equation is constant in time. A general formula is given for time evolution of fluctuations of the invariants. An application to the problem of share price in finance is illustrated. It is shown how this theory makes it possible to reduce the growth rate of the fluctuations.
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Jinno, Ryusuke; Mukaida, Kyohei; Nakayama, Kazunori
2015-01-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is us...
Computer calculation of Witten's 3-manifold invariant
Freed, Daniel S.; Gompf, Robert E.
1991-10-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.
Rotational invariance and the Pauli exclusion principle
O'Hara, Paul
2001-01-01
In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence...
The invariator principle in convex geometry
DEFF Research Database (Denmark)
Thórisdóttir, Ólöf; Kiderlen, Markus
The invariator principle is a measure decomposition that was rediscovered in local stereology in 2005 and has since been used widely in the stereological literature. We give an exposition of invariator related results where existing formulae are generalized and new ones proposed. In particular, w...... functions and derive several, more explicit representations of these functions. In particular, we use Morse theory to write the measurement functions in terms of critical values of the sectioned object. This is very useful for surface area estimation....
Weyl Invariance and the Origins of Mass
Gover, A R; Waldron, A
2008-01-01
By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner-Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus -- mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.
Complete simultaneous conjugacy invariants in Garside groups
Kalka, Arkadius; Tsaban, Boaz; Vinokur, Gary
2014-01-01
We solve the simultaneous conjugacy problem in Garside groups, by means of an effectively computable invariant. In the one-dimensional case, our invariant generalizes the notion of super summit set of a conjugacy class. As part of our solution, we identify a high-dimensional version of the cyclic sliding operation with a provable convergence rate. The complexity of this solution is a small degree polynomial in the sizes of our generalized super summit sets and the input parameters. Computer e...
Invariant Spectral Hashing of Image Saliency Graph
Taquet, Maxime; Jacques, Laurent; De Vleeschouwer, Christophe; Macq, Benoît
2010-01-01
Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image....
The Fundamental Theorem of Vassiliev Invariants
Bar-Natan, Dror; STOIMENOW, Alexander
1997-01-01
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M. Hutchings, a geometrical approach following Kontsevich, an algebraic approach following Drinfel'd's theory of associators, and a physical approach coming from the Chern-Simons quantum field theory. Each of these approaches is unsatisfactory in one way or anothe...
On the -Invariant of Hermitian Forms
Indian Academy of Sciences (India)
Sudeep S Parihar; V Suresh
2013-08-01
Let be a field of characteristic not 2 and a central simple algebra with an involution . A result of Mahmoudi provides an upper bound for the -invariants of hermitian forms and skew-hermitian forms over (,) in terms of the -invariant of . In this paper we give a different upper bound when is a tensor product of quaternion algebras and is a the tensor product of canonical involutions. We also show that our bounds are sharper than those of Mahmoudi.
Auto-pooling: Learning to Improve Invariance of Image Features from Image Sequences
Sukhbaatar, Sainbayar; Makino, Takaki; Aihara, Kazuyuki
2013-01-01
Learning invariant representations from images is one of the hardest challenges facing computer vision. Spatial pooling is widely used to create invariance to spatial shifting, but it is restricted to convolutional models. In this paper, we propose a novel pooling method that can learn soft clustering of features from image sequences. It is trained to improve the temporal coherence of features, while keeping the information loss at minimum. Our method does not use spatial information, so it c...
Helicity is the only integral invariant of volume-preserving transformations
Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres
2016-01-01
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional $\\mathcal I$ defined on exact divergence-free vector fields of class $C^1$ on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\\mathcal I$ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.
Page, Don N.
2008-01-01
VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants (nonpolynomial) from the Riemann tensor that need not vanish even in VSI spacetimes, such as Cartan invariants. Simple examples are given that reduce to the squared amplitude for a linearized monochromatic plane gravitational wave. These nonpolynomial local sc...
Search for anisotropic Lorentz invariance violation with γ -rays
Kislat, Fabian; Krawczynski, Henric
2015-08-01
While Lorentz invariance, the fundamental symmetry of Einstein's theory of general relativity, has been tested to a great level of detail, grand unified theories that combine gravity with the other three fundamental forces may result in a violation of Lorentz symmetry at the Planck scale. These energies are unattainable experimentally. However, minute deviations from Lorentz invariance may still be present at much lower energies. These deviations can accumulate over large distances, making astrophysical measurements the most sensitive tests of Lorentz symmetry. One effect of Lorentz invariance violation is an energy-dependent photon dispersion of the vacuum resulting in differences of the light travel time from distant objects. The Standard Model Extension (SME) is an effective theory to describe the low-energy behavior of a more fundamental grand unified theory, including Lorentz- and C P T -violating terms. In the SME the Lorentz-violating operators can in part be classified by their mass dimension d , with the lowest order being d =5 . However, measurements of photon polarization have constrained operators with d =5 setting lower limits on the energy at which they become dominant well beyond the Planck scale. On the other hand, these operators also violate C P T , and thus d =6 could be the leading order. In this paper we present constraints on all 25 real coefficients describing anisotropic nonbirefringent Lorentz invariance violation at mass dimension d =6 in the SME. We used Fermi-LAT observations of 25 active galactic nuclei to constrain photon dispersion and combined our results with previously published limits in order to simultaneously constrain all 25 coefficients. This represents the first set of constraints on these coefficients of mass dimension d =6 , whereas previous measurements were only able to constrain linear combinations of all 25 coefficients.
On gauge-invariant and phase-invariant spinor analysis. II
Buchdahl, H. A.
1992-01-01
Granted customary definitions, the operations of juggling indices and covariant differentiation do not commute with one another in a Weyl space. The same noncommutativity obtains in the spinor calculus of Infeld and van der Waerden. Gauge-invariant and phase-invariant calculations therefore tend to be rather cumbersome. Here, a modification of the definition of covariant derivative leads immediately to a manifestly gauge-invariant and phase-invariant version of Weyl-Cartan space and of the two-spinor calculus associated with it in which the metric tensor and the metric spinor are both covariant constant.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, J
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.
On the statistics of magnetotelluric rotational invariants
Chave, Alan D.
2014-01-01
The statistical properties of the Swift skew, the phase-sensitive skew and the WAL invariants I1-I7 and Q are examined through analytic derivation of their probability density functions and/or simulation based on a Gaussian model for the magnetotelluric response tensor. The WAL invariants I1-I2 are shown to be distributed as a folded Gaussian, and are statistically well behaved in the sense that all of their moments are defined. The probability density functions for Swift skew, phase-sensitive skew and the WAL invariants I3-I4, I7 and Q are derived analytically or by simulation, and are shown to have no moments of order 2 or more. Since their support is semi-infinite or infinite, they cannot be represented trigonometrically, and hence are inconsistent with a Mohr circle interpretation. By contrast, the WAL invariants I5-I6 are supported on [ - 1, 1], and are inferred to have a beta distribution based on analysis and simulation. Estimation of rotational invariants from data is described using two approaches: as the ratio of magnetotelluric responses that are themselves averages, and as averages of section-by-section estimates of the invariant. Confidence intervals on the former utilize either Fieller's theorem, which is preferred because it is capable of yielding semi-infinite or infinite confidence intervals, or the less accurate delta method. Because section-by-section averages of most of the rotational invariants are drawn from distributions with infinite variance, the classical central limit theorem does not pertain. Instead, their averaging is accomplished using the median in place of the mean for location and an order statistic model to bound the confidence interval of the median. An example using real data demonstrates that the ratio of averages approach has serious systematic bias issues that render the result physically inconsistent, while the average of ratios result is a smooth, physically interpretable function of period, and is the preferred approach.
Invariant object recognition based on extended fragments.
Bart, Evgeniy; Hegdé, Jay
2012-01-01
Visual appearance of natural objects is profoundly affected by viewing conditions such as viewpoint and illumination. Human subjects can nevertheless compensate well for variations in these viewing conditions. The strategies that the visual system uses to accomplish this are largely unclear. Previous computational studies have suggested that in principle, certain types of object fragments (rather than whole objects) can be used for invariant recognition. However, whether the human visual system is actually capable of using this strategy remains unknown. Here, we show that human observers can achieve illumination invariance by using object fragments that carry the relevant information. To determine this, we have used novel, but naturalistic, 3-D visual objects called "digital embryos." Using novel instances of whole embryos, not fragments, we trained subjects to recognize individual embryos across illuminations. We then tested the illumination-invariant object recognition performance of subjects using fragments. We found that the performance was strongly correlated with the mutual information (MI) of the fragments, provided that MI value took variations in illumination into consideration. This correlation was not attributable to any systematic differences in task difficulty between different fragments. These results reveal two important principles of invariant object recognition. First, the subjects can achieve invariance at least in part by compensating for the changes in the appearance of small local features, rather than of whole objects. Second, the subjects do not always rely on generic or pre-existing invariance of features (i.e., features whose appearance remains largely unchanged by variations in illumination), and are capable of using learning to compensate for appearance changes when necessary. These psychophysical results closely fit the predictions of earlier computational studies of fragment-based invariant object recognition. PMID:22936910
Invariant Object Recognition Based on Extended Fragments
Directory of Open Access Journals (Sweden)
Evgeniy eBart
2012-08-01
Full Text Available Visual appearance of natural objects is profoundly affected by viewing conditions such as viewpoint and illumination. Human subjects can nevertheless compensate well for variations in these viewing conditions. The strategies that the visual system uses to accomplish this are largely unclear. Previous computational studies have suggested that in principle, certain types of object fragments (rather than whole objects can be used for invariant recognition. However, whether the human visual system is actually capable of using this strategy remains unknown. Here, we show that human observers can achieve illumination invariance by using object fragments that carry the relevant information. To determine this, we have used novel, but naturalistic, 3-D visual objects called ‘digital embryos’. Using novel instances of whole embryos, not fragments, we trained subjects to recognize individual embryos across illuminations. We then tested the illumination-invariant object recognition performance of subjects using fragments. We found that the performance was strongly correlated with the mutual information (MI of the fragments, provided that MI value took variations in illumination into consideration. This correlation was not attributable to any systematic differences in task difficulty between different fragments. These results reveal two important principles of invariant object recognition. First, the subjects can achieve invariance at least in part by compensating for the changes in the appearance of small local features, rather than of whole objects. Second, the subjects do not always rely on generic or pre-existing invariance of features (i.e., features whose appearance remains largely unchanged by variations in illumination, and are capable of using learning to compensate for appearance changes when necessary. These psychophysical results closely fit the predictions of earlier computational studies of fragment-based invariant object recognition.
Asymptotic distribution of the most powerful invariant test for invariant families
Arcones, Miguel A.
2009-01-01
We obtain the limit distribution of the test statistic of the most powerful invariant test for location families of densities. As an application, we obtain the consistency of this test. From these results similar results are obtained for the test statistic of the most powerful invariant test for scale families.
Buchstaber numbers and classical invariants of simplicial complexes
Ayzenberg, Anton
2014-01-01
Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial complexes such as bigraded Betti numbers and chromatic invariants. The following two statements are proved. (1) There exists a simplicial complex U with different real and ordinary Buchstaber invariants. (2) There exist two simplicial complexes with equal bigrade...
A Unified Framework for Verification Techniques for Object Invariants
Drossopoulou, Sophia; Francalanza, Adrian; Müller, P; Summers, Alexander J.
2008-01-01
Object invariants define the consistency of objects. They have subtle semantics, mainly because of call-backs, multi-object invariants, and subclassing. Several verification techniques for object invariants have been proposed. It is difficult to compare these techniques, and to ascertain their soundness, because of their differences in restrictions on programs and invariants, in the use of advanced type systems (e.g., ownership types), in the meaning of invariants, and in...
Scale-Invariant Random Spatial Networks
Aldous, David J
2012-01-01
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\\em exactly} invariant under Euclidean scaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call {\\em scale-invariant random spatial networks}, whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class.
Second-Order Invariants and Holography
Luongo, Orlando; Bonanno, Luca; Iannone, Gerardo
2012-12-01
Motivated by recent works on the role of the holographic principle in cosmology, we relate a class of second-order Ricci invariants to the IR cutoff characterizing the holographic dark energy density. The choice of second-order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an a priori assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.
Hidden Scale Invariance in Condensed Matter
DEFF Research Database (Denmark)
Dyre, J. C.
2014-01-01
Recent developments show that many liquids and solids have an approximate “hidden” scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This...... (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments...... means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding...
Rainbow gravity and scale-invariant fluctuations
Amelino-Camelia, Giovanni; Arzano, Michele; Gubitosi, Giulia; Magueijo, João
2013-08-01
We reexamine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable “rainbow frame” this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behavior of gravity under the phenomenon of dimensional reduction.
Thermodynamics and time-directional invariance
Klimenko, A Y
2012-01-01
Time directions are not invariant in conventional thermodynamics. We broadly follow ideas of Ludwig Boltzmann and investigate implications of postulating time-directional invariance in thermodynamics. In this investigation, we require that thermodynamic descriptions are not changed under time reversal accompanied by replacement of matter by antimatter (i.e. CPT-invariant thermodynamics). The matter and antimatter are defined as thermodynamic concepts without detailing their physical structure. Our analysis stays within the limits of conceptual thermodynamics and leads to effective negative temperatures, to thermodynamic restrictions on time travel and to inherent antagonism of matter and antimatter. This antagonism is purely thermodynamic; it explains the difficulty in achieving thermodynamic equilibrium between matter and antimatter and does not postulate their mutual annihilation on contact. We believe that the conclusions of this work can be of interest not only for people researching or teaching thermodyn...
Manifestly diffeomorphism invariant classical Exact Renormalization Group
Morris, Tim R
2016-01-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renormalization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeomorphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
Rainbow gravity and scale-invariant fluctuations
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Magueijo, Joao
2013-01-01
We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays a wavelength-dependent speed of light but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale-invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behaviour of gravity under the phenomenon of dimensional reduction.
Gauge-invariant massive BF models
Bizdadea, Constantin
2015-01-01
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, Poincare invariance, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field $A_{\\mu }$ with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking.