Lectures on Conformal Field Theory arXiv:1511.04074v2 [hep
... In Lecture 2, we study the basic properies of CFTs in d > 2 dimensions. Topics include conformal transformations, their infinitesimal form, a detailed discussion of special conformal transformations, the conformal algebra and group, and representations of the conformal group. We next discuss constr ...
... In Lecture 2, we study the basic properies of CFTs in d > 2 dimensions. Topics include conformal transformations, their infinitesimal form, a detailed discussion of special conformal transformations, the conformal algebra and group, and representations of the conformal group. We next discuss constr ...
A short review on Noether`s theorems, gauge
... Any function δs q i (t) that satisfies (2.5) represents a symmetry. Eqn. (2.5) must be understood as an equation for δs q i (t). If, for a given action I[q i (t)], we find all functions δs q i (t) satisfying (2.5), then we have solved the equations of motion of the problem. The central force problem ...
... Any function δs q i (t) that satisfies (2.5) represents a symmetry. Eqn. (2.5) must be understood as an equation for δs q i (t). If, for a given action I[q i (t)], we find all functions δs q i (t) satisfying (2.5), then we have solved the equations of motion of the problem. The central force problem ...
Multidimensional Hypergeometric Functions in Conformai Field
... (ßL = dln(z1/z0) over a path going from M1 to M 0 . flj(L;M) is equal to the logarithm of the cross ratio of the four points (L 0 , Ll9 M0, Mx). The Euler dilogarithm is a special case of the Aomoto dilogarithm, see Fig. 1. There are two connections of polylogarithms of different orders: the multipl ...
... (ßL = dln(z1/z0) over a path going from M1 to M 0 . flj(L;M) is equal to the logarithm of the cross ratio of the four points (L 0 , Ll9 M0, Mx). The Euler dilogarithm is a special case of the Aomoto dilogarithm, see Fig. 1. There are two connections of polylogarithms of different orders: the multipl ...
Black-hole/near-horizon-CFT duality and 4 dimensional classical
... limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. L ...
... limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. L ...
Mathematisches Forschungsinstitut Oberwolfach Subfactors and
... The idea of obtaining a “continuum limit” by letting the number of boundary points on the discs fill out the circle has been around for over 20 years but this paper is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the not ...
... The idea of obtaining a “continuum limit” by letting the number of boundary points on the discs fill out the circle has been around for over 20 years but this paper is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the not ...
Exactly Solvable Problems in Quantum Mechanics
... Having all this in mind, one is strongly tempted to conclude that any existing case of exact solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods a ...
... Having all this in mind, one is strongly tempted to conclude that any existing case of exact solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods a ...
pdf - at www.arxiv.org.
... CFTs in this way. As an attempt to find a systematic and controlled construction of such deformations, we will make use of conformal mapping. Our construction can be described as follows: (i) We start from a reference (1+1)-dimensional spacetime, parameterized by a complex coordinate which is denote ...
... CFTs in this way. As an attempt to find a systematic and controlled construction of such deformations, we will make use of conformal mapping. Our construction can be described as follows: (i) We start from a reference (1+1)-dimensional spacetime, parameterized by a complex coordinate which is denote ...
L. Fortunato - INFN Padova
... then G is called spectrum generating algebra (SGA) for H, because it is always possible to diagonalize (numerically) H in the ONC basis labelled by all the quantum numbers of a Complete Set of Commuting Operators (CSCO) of any of the possible chains of subalgebras of G G’ G’’ … Once the action ...
... then G is called spectrum generating algebra (SGA) for H, because it is always possible to diagonalize (numerically) H in the ONC basis labelled by all the quantum numbers of a Complete Set of Commuting Operators (CSCO) of any of the possible chains of subalgebras of G G’ G’’ … Once the action ...
Classical elliptic current algebras
... a quantization of certain (twisted) Manin pairs [ER1] using Drinfeld’s new realization of quantized current algebras. Further, it was shown in [EF] that the Felder algebra can be obtained by twisting of the Enriquez-Rubtsov elliptic algebra. This twisted algebra will be denoted by Eτ,η and it is a q ...
... a quantization of certain (twisted) Manin pairs [ER1] using Drinfeld’s new realization of quantized current algebras. Further, it was shown in [EF] that the Felder algebra can be obtained by twisting of the Enriquez-Rubtsov elliptic algebra. This twisted algebra will be denoted by Eτ,η and it is a q ...
M04/16
... is an effect algebra. In many cases, these intervals preserve the properties of E. The concepts of local and global sharpness of measurements are introduced. In Section 4 we study measurements with finitely many real values which we call finite measurements. Denoting the set of finite measurements by MF ...
... is an effect algebra. In many cases, these intervals preserve the properties of E. The concepts of local and global sharpness of measurements are introduced. In Section 4 we study measurements with finitely many real values which we call finite measurements. Denoting the set of finite measurements by MF ...
PROJECTIVE AND CONFORMAL STRUCTURES IN GENERAL
... If the microcavity is the right width, the energies of the cavity photon and the exciton can be made to match up. When this happens the two mix, forming a new particle. This is a combination of matter and electromagnetic waves — an exciton-polariton, or simply 'polariton'. These polaritons inherit s ...
... If the microcavity is the right width, the energies of the cavity photon and the exciton can be made to match up. When this happens the two mix, forming a new particle. This is a combination of matter and electromagnetic waves — an exciton-polariton, or simply 'polariton'. These polaritons inherit s ...
Table des mati`eres 1 Technical and Scientific description of
... The one-parameter groups of these transformations have infinitesimal generators that are vector fields and their conjugates [19]. On the other hand, computation necessities forced us to initiate this program by computing on Taylor series. This led us to the evidence that the group of substitution wi ...
... The one-parameter groups of these transformations have infinitesimal generators that are vector fields and their conjugates [19]. On the other hand, computation necessities forced us to initiate this program by computing on Taylor series. This led us to the evidence that the group of substitution wi ...
Does Geometric Algebra provide a loophole to Bell`s Theorem?
... Gill (2012), of one of Christian’s shortest papers: the so-called “one page paper”, Christian (2011), which moreover contains the substance of the first chapter of Christian’s book. In the present paper he analyses in the same spirit the paper Christian (2007), which was the foundation or starting s ...
... Gill (2012), of one of Christian’s shortest papers: the so-called “one page paper”, Christian (2011), which moreover contains the substance of the first chapter of Christian’s book. In the present paper he analyses in the same spirit the paper Christian (2007), which was the foundation or starting s ...
Topological structures in string theory
... defined by a pair of pants, is a weighted compromise between ordinary pointwise multiplication and convolution with respect to concatenating the loops. To make precise sense of this schematic picture requires all the technology of two-dimensional quantum field theory, but the belief that underlies str ...
... defined by a pair of pants, is a weighted compromise between ordinary pointwise multiplication and convolution with respect to concatenating the loops. To make precise sense of this schematic picture requires all the technology of two-dimensional quantum field theory, but the belief that underlies str ...
Modified Weak Energy Condition for the Energy Momentum Tensor
... values of the the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states |ψi for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural res ...
... values of the the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states |ψi for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural res ...
Notes on 2d quantum gravity and Liouville theory - lpthe
... 5.4 Few properties of the classical Liouville action . . . . . . . . . . . . . . . . 5.4.1 Central charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Polyakov action and critical string theory . . . . . . . . . . . . . . 5.5 Changing the Liouville mode measure . . . . . . . . . . ...
... 5.4 Few properties of the classical Liouville action . . . . . . . . . . . . . . . . 5.4.1 Central charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Polyakov action and critical string theory . . . . . . . . . . . . . . 5.5 Changing the Liouville mode measure . . . . . . . . . . ...
Thermal equilibrium states for quantum fields on
... at hand, the effect of the noncommutativity parameter θ on scattering processes (at zero temperature) was investigated in [GL07], and shown to lead to modifications in the phase shift of two-particle scattering. Here we ask in the same model “what are the observational consequences of a non-commutat ...
... at hand, the effect of the noncommutativity parameter θ on scattering processes (at zero temperature) was investigated in [GL07], and shown to lead to modifications in the phase shift of two-particle scattering. Here we ask in the same model “what are the observational consequences of a non-commutat ...
L. Snobl: Representations of Lie algebras, Casimir operators and
... The commutator (18) prevents the operators L̂j , K̂j from forming a Lie algebra. Nevertheless, this bothersome property can be circumvented if we consider a given energy level, i.e. a subspace HE of the Hilbert space H consisting of all eigenvectors of Ĥ with the given energy E. Operators L̂j , K̂j ...
... The commutator (18) prevents the operators L̂j , K̂j from forming a Lie algebra. Nevertheless, this bothersome property can be circumvented if we consider a given energy level, i.e. a subspace HE of the Hilbert space H consisting of all eigenvectors of Ĥ with the given energy E. Operators L̂j , K̂j ...
Algebra in Braided Tensor Categories and Conformal Field Theory
... category of such representations is a symmetric tensor category, which contains a subcategory equivalent to the category G-mod of finite dimensional continuous unitary representations of a compact group G. The group G gives the global symmetries of the QFT. In fact, from the knowledge of the supers ...
... category of such representations is a symmetric tensor category, which contains a subcategory equivalent to the category G-mod of finite dimensional continuous unitary representations of a compact group G. The group G gives the global symmetries of the QFT. In fact, from the knowledge of the supers ...
Light-like -deformations and scalar field theory via Drinfeld twist
... Abelian [9, 8] and Jordanian twist [10], but the problem with these twists is that they can not be expressed in terms of the Poincaré generators only. The κ-Poincaré-Hopf algebra was obtained using a twist in a Hopf algebroid approach in [11]. Particularly, a full description of deformation of Poi ...
... Abelian [9, 8] and Jordanian twist [10], but the problem with these twists is that they can not be expressed in terms of the Poincaré generators only. The κ-Poincaré-Hopf algebra was obtained using a twist in a Hopf algebroid approach in [11]. Particularly, a full description of deformation of Poi ...
Reflection equation algebra in braided geometry 1
... super-flip then P− (t) = (1+t) (1−t)r . Definition 2.3. If P− (t) (respectively P+ (t)) is a monic polynomial then the space V and the braiding R are called even (respectively odd). Theorem 2.4. If R is even then the polynomial P− (t) is reciprocal. Proposition 2.5. For any V with dimV = n ≥ 2 there ...
... super-flip then P− (t) = (1+t) (1−t)r . Definition 2.3. If P− (t) (respectively P+ (t)) is a monic polynomial then the space V and the braiding R are called even (respectively odd). Theorem 2.4. If R is even then the polynomial P− (t) is reciprocal. Proposition 2.5. For any V with dimV = n ≥ 2 there ...
Geometrical Aspects of Conformal Quantum Field Theory
... model is used to give mass to the gauge bosons of the weak interaction, it should naturally possess a mass near the weak breaking scale. It can be shown that a Higgs mass beyond ≈ 1 TeV renders the symmetry breaking inconsistent. The hierarchy problem arises when one considers corrections to this ma ...
... model is used to give mass to the gauge bosons of the weak interaction, it should naturally possess a mass near the weak breaking scale. It can be shown that a Higgs mass beyond ≈ 1 TeV renders the symmetry breaking inconsistent. The hierarchy problem arises when one considers corrections to this ma ...
Unparticle_Dark_Matter_(GUT07)
... • Beyond the SM (for model buildings in this LHC era): Are there totally unexpected phenomena which has not yet discovered so far? What would be expected to happen at LHC that might be originated from some unknown models, not only SUSY or extra dimensional models, etc.? This is basically the motivat ...
... • Beyond the SM (for model buildings in this LHC era): Are there totally unexpected phenomena which has not yet discovered so far? What would be expected to happen at LHC that might be originated from some unknown models, not only SUSY or extra dimensional models, etc.? This is basically the motivat ...
Operator Algebras and Index Theorems in Quantum Field Theory
... Final comment. It would be interesting to relate our setting with Connes’ Noncommutative Geometry. A link should be possible in a supersymmetric context, where cyclic cohomology appears. In this respect model analysis with our point of view, in particular in the supersymmetric frame, may be of inte ...
... Final comment. It would be interesting to relate our setting with Connes’ Noncommutative Geometry. A link should be possible in a supersymmetric context, where cyclic cohomology appears. In this respect model analysis with our point of view, in particular in the supersymmetric frame, may be of inte ...