Non-Pauli Effects from Noncommutative Spacetimes

Noncommutative spacetimes lead to nonlocal quantum field theories (qft's) where spin-statistics theorems cannot be proved. For this reason, and also backed by detailed arguments, it has been suggested that they get corrected on such spacetimes leading to small violations of the Pauli principle. In a recent paper \cite{Pauli}, Pauli-forbidden transitions from spacetime noncommutativity were calculated and confronted with experiments. Here we give details of the computation missing from this paper. The latter was based on a spacetime $\mathcal{B}_{\chi\vec{n}}$ different from the Moyal plane. We argue that it quantizes time in units of $\chi$. Energy is then conserved only mod $\frac{2\pi}{\chi}$. Issues related to superselection rules raised by non-Pauli effects are also discussed in a preliminary manner.Comment: 15 Pages, 1 Table, Full details and further developments of arXiv:1003.2250. This version is close to the one accepted by JHE

Hidden Yangian symmetry in sigma model on squashed sphere

We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and show the Yangian algebra by directly checking the Serre relation. This symmetry is also deduced from the coset structure of the squashed sphere. The same argument is applicable to the warped AdS_3 spaces via double Wick rotations.Comment: 11 pages, 1 figure, typos corrected, references adde

Twisted Yangians for symmetric pairs of types B, C, D

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for orthogonal or symplectic Lie algebras. They can also be presented as quotients of a reflection algebra by additional symmetry relations. We prove an analogue of the Poincare-Birkoff-Witt Theorem, determine their centres and study also extended reflection algebras

Young tableaux and crystal B(∞)B(\infty) for finite simple Lie algebras

We study the crystal base of the negative part of a quantum group. An explicit realization of the crystal is given in terms of Young tableaux for types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$. Connection between our realization and a previous realization of Cliff is also given

Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry

We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R due to the deformation. According to this symmetry, there are two descriptions to describe the classical dynamics of the system, 1) the SL(2,R)_L description and 2) the enhanced U(1)_R description. In the former 1), we show that the Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a Lax pair is constructed with the improved current and the classical integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we find a non-local current by using a scaling limit of warped AdS_3 and that it enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is presented and the corresponding r/s-matrices are also computed. The two descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde

Very special relativity as relativity of dark matter: the Elko connection

In the very special relativity (VSR) proposal by Cohen and Glashow, it was pointed out that invariance under HOM(2) is both necessary and sufficient to explain the null result of the Michelson-Morely experiment. It is the quantum field theoretic demand of locality, or the requirement of P, T, CP, or CT invariance, that makes invariance under the Lorentz group a necessity. Originally it was conjectured that VSR operates at the Planck scale; we propose that the natural arena for VSR is at energies similar to the standard model, but in the dark sector. To this end we provide an ab initio spinor representation invariant under the SIM(2) avatar of VSR and construct a mass dimension one fermionic quantum field of spin one half. This field turns out to be a very close sibling of Elko and it exhibits the same striking property of intrinsic darkness with respect to the standard model fields. In the new construct, the tension between Elko and Lorentz symmetries is fully resolved. We thus entertain the possibility that the symmetries underlying the standard model matter and gauge fields are those of Lorentz, while the event space underlying the dark matter and the dark gauge fields supports the algebraic structure underlying VSR.Comment: 19 pages. Section 5 is new. Published version (modulo a footnote, and a corrected typo

The Relativistic Avatars of Giant Magnons and their S-Matrix

The motion of strings on symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although these theories, whose excitations are giant magnons, are non-relativistic they are classically equivalent, via the Polhmeyer reduction, to a relativistic integrable field theory known as a symmetric space sine-Gordon theory. These theories can be formulated as integrable deformations of gauged WZW models. In this work we consider the class of symmetric spaces CP^{n+1} and solve the corresponding generalized sine-Gordon theories at the quantum level by finding the exact spectrum of topological solitons, or kinks, and their S-matrix. The latter involves a trignometric solution of the Yang-Baxer equation which exhibits a quantum group symmetry with a tower of states that is bounded, unlike for magnons, as a result of the quantum group deformation parameter q being a root of unity. We test the S-matrix by taking the semi-classical limit and comparing with the time delays for the scattering of classical solitons. We argue that the internal CP^{n-1} moduli space of collective coordinates of the solitons in the classical theory can be interpreted as a q-deformed fuzzy space in the quantum theory. We analyse the n=1 case separately and provide a further test of the S-matrix conjecture in this case by calculating the central charge of the UV CFT using the thermodynamic Bethe Ansatz.Comment: 33 pages, important correction to S-matrix to ensure crossing symmetr

Equivalences between three presentations of orthogonal and symplectic Yangians

We prove the equivalence of two presentations of the Yangian $Y(\mathfrak{g})$ of a simple Lie algebra $\mathfrak{g}$ and we also show the equivalence with a third presentation when $\mathfrak{g}$ is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians

Deformation quantisation for unshifted symplectic structures on derived Artin stacks

We prove that every $0$-shifted symplectic structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation. The classical method of quantising smooth varieties via quantisations of affine space does not apply in this setting, so we develop a new approach. We construct a map from DQ algebroid quantisations of unshifted symplectic structures on a derived Artin $n$-stack to power series in de Rham cohomology, depending only on a choice of Drinfeld associator. This gives an equivalence between even power series and certain involutive quantisations, which yield anti-involutive curved $A_{\infty}$ deformations of the dg category of perfect complexes. In particular, there is a canonical quantisation associated to every symplectic structure on such a stack, which agrees for smooth varieties with the Kontsevich--Tamarkin quantisation for even associators.Comment: 27pp.; v2 Propositions 1.23 and 3.10 added; v3 several small additions; v4 several changes following referee's comments, to appear in Select

Suicide among persons with childhood leukaemia in Slovenia

Pri osebah, ki so v otroštvu zbolele za rakom, so pogosto prisotne telesne in psihosocialne posledice bolezni ter njenega zdravljenja. Mnoge raziskave so pokazale, da je pri osebah z izkušnjo raka v otroštvu depresivnost in samomorilno vedenje močneje izraženo. V naši raziskavi smo proučili pojavljanje samomorov pri osebah, ki so v otroštvu zbolele za levkemijo, v primerjavi s splošno populacijo v Sloveniji, v obdobju 1978–2010. Pričakovano število samomorov smo izračunali na osnovi kontrolne skupine posameznikov iz splošne populacije, ki je bila s skupino preiskovancev, tj. oseb, ki so v otroštvu zbolele za levkemijo, izenačena po spolu, starosti ob začetku opazovanja, letu začetka opazovanja in dolžini opazovanja. Raziskava je pokazala, da med tistimi, ki so v otroštvu zboleli za levkemijo, v letih 1978–2010 nobena oseba ni storila samomora, kar se statistično značilno ne razlikuje od pričakovanega števila samomorov (0,448) v primerljivi splošni populaciji v Sloveniji. Ugotovitve raziskave nakazujejo, da kljub znano bolj izraženem samomorilnem vedenju med preživelimi raka v otroštvu v Sloveniji v primerjavi s splošno populacijo pojavljanje samomorov pri osebah, zbolelih za levkemijo v otroštvu, ni pogostejše kot v splošni populaciji.Persons with childhood leukaemia often suffer from physical and psychosocial consequences of the disease and its treatment. Several studies have shown that depression and suicidal behaviour are expressed strongly in persons with a childhood cancer experience. In our study, we researched the occurrence of suicides among persons with childhood leukaemia compared to the general population in Slovenia in the period 1978–2010. The expected number of suicides was calculated based on the control group of individuals from the general population with the same gender, age at the beginning of observation, starting year and duration of observation as the research group, thus group of persons with childhood cancer. The study showed that none of the persons with childhood cancer committed suicide in the period 1978-2010, which is not statistically different from the expected number of suicides (0.448) in comparison with the general population in Slovenia. The findings of this study indicate that, despite the significantly increased expression of suicidal behaviour among survivors of childhood leukaemia in Slovenia compared to the general population, suicides do not occur more often among people with childhood leukaemia than among the general population