Quantum field theory correlators at very short and very long distances

... Why deSitter space? DeSitter space describes the era of “inflation”, which is characterized by a very large cosmological constant Λ of the order of the GUT scale. Λ arises from potential energy of the inflaton field (?). It is currently believed that the current accelerated expansion of the universe ...

... Why deSitter space? DeSitter space describes the era of “inflation”, which is characterized by a very large cosmological constant Λ of the order of the GUT scale. Λ arises from potential energy of the inflaton field (?). It is currently believed that the current accelerated expansion of the universe ...

Factorization Algebras in Quantum Field Theory Volume 1 (8 May

... record how the measurement device has modified from its initial condition. (Of course, there is a symmetry in this situation: both systems are affected by their interaction, so a measurement inherently disturbs the system under study.) The observables for a physical system are all the imaginable mea ...

... record how the measurement device has modified from its initial condition. (Of course, there is a symmetry in this situation: both systems are affected by their interaction, so a measurement inherently disturbs the system under study.) The observables for a physical system are all the imaginable mea ...

Thèse de doctorat - IMJ-PRG

... Abstract The main part of this thesis is devoted to study some constructions and structures around quantum shuffle algebras: differential algebras and Kashiwara operators; defining ideals and specialization problem; coHochschild homology and an analogue of Borel-Weil-Bott theorem. In the last chapte ...

... Abstract The main part of this thesis is devoted to study some constructions and structures around quantum shuffle algebras: differential algebras and Kashiwara operators; defining ideals and specialization problem; coHochschild homology and an analogue of Borel-Weil-Bott theorem. In the last chapte ...

An Introduction to the Theory of Quantum Groups

... weirdness surrounding the discoveries of quantum physics. So, just what are these exciting new structures called quantum groups? It’s always good to be honest at the outset of a significant undertaking. With that said, the reader might be disappointed to learn that there is no rigorous, universally ...

... weirdness surrounding the discoveries of quantum physics. So, just what are these exciting new structures called quantum groups? It’s always good to be honest at the outset of a significant undertaking. With that said, the reader might be disappointed to learn that there is no rigorous, universally ...

Entanglement Entropy of non-Unitary Quantum Field Theory

... Suppose that we are given a pure state |ψi and that we perform a computation of the EE. If we find logarithmic scaling we may deduce that the system is critical and we expect to be able to extract the central charge c of the critical point. What happens if |ψi is the ground state of a critical syste ...

... Suppose that we are given a pure state |ψi and that we perform a computation of the EE. If we find logarithmic scaling we may deduce that the system is critical and we expect to be able to extract the central charge c of the critical point. What happens if |ψi is the ground state of a critical syste ...

Quantum groups: A survey of de nitions, motivations, and results

... complete set of ideas without disrupting any particular section with a myriad of lengthy de nitions. Even though we may wish it so, ideas in mathematics are not really linear and this has been reected in these notes. The reader should feel free to skip around in the notes whenever the inclination a ...

... complete set of ideas without disrupting any particular section with a myriad of lengthy de nitions. Even though we may wish it so, ideas in mathematics are not really linear and this has been reected in these notes. The reader should feel free to skip around in the notes whenever the inclination a ...

Quantum Groups: A Path to Current Algebra

... Now we are ready to formalize duality. Given a projective plane P , we obtain a projective plane P rev whose points are the lines of P , whose lines are the points of P , and whose incidence relation is the reverse of that of P . Notice that axioms (1) and (2) for P rev are respectively axioms (2) a ...

... Now we are ready to formalize duality. Given a projective plane P , we obtain a projective plane P rev whose points are the lines of P , whose lines are the points of P , and whose incidence relation is the reverse of that of P . Notice that axioms (1) and (2) for P rev are respectively axioms (2) a ...

Symmetry and symmetry breaking, algebraic approach to - IME-USP

... The discovery of the molecular structure of DNA by Watson and Crick in 19531,2 is one of the landmarks in the history of science. The substance itself had been known since 1869 and had been recognized as the carrier of genetic information in 1944, but the basis of its biological function, of its sta ...

... The discovery of the molecular structure of DNA by Watson and Crick in 19531,2 is one of the landmarks in the history of science. The substance itself had been known since 1869 and had been recognized as the carrier of genetic information in 1944, but the basis of its biological function, of its sta ...

Factorization algebras and free field theories

... Chapter 2 is an introduction to the BV formalism for “0-dimensional field theories,” namely when the space of fields M is in fact a finite-dimensional manifold. We begin by extracting the axiomatics from familiar constructions in geometry. We then explain how to recover Wick’s lemma and Feynman diag ...

... Chapter 2 is an introduction to the BV formalism for “0-dimensional field theories,” namely when the space of fields M is in fact a finite-dimensional manifold. We begin by extracting the axiomatics from familiar constructions in geometry. We then explain how to recover Wick’s lemma and Feynman diag ...

Entanglement Spectrum in the Fractional Quantum Hall Effect

... In particular the FQHE exhibits a new type of order different from the classical or quantum orders that can be described by the paradigm of Landau’s symmetry breaking theory. This new type of order is robust upon local perturbations and cannot be described by a symmetry or a broken symmetry. In part ...

... In particular the FQHE exhibits a new type of order different from the classical or quantum orders that can be described by the paradigm of Landau’s symmetry breaking theory. This new type of order is robust upon local perturbations and cannot be described by a symmetry or a broken symmetry. In part ...

Supersymmetry (SUSY)

... A Lie group containing the Poincare group and an internal group, e.g. the Standard Model gauge group, will be formed by the direct product: ...

... A Lie group containing the Poincare group and an internal group, e.g. the Standard Model gauge group, will be formed by the direct product: ...

PARADIGM OF QUASI-LIE AND QUASI-HOM

... quantum inverse scattering methods [25]. This method developed by L.D. Faddeev and his collaborators gave rise to a great interest in quantum groups and Hopf algebras. Since then several other versions of (q-) deformed Lie algebras have appeared, especially in physical contexts such as string theory ...

... quantum inverse scattering methods [25]. This method developed by L.D. Faddeev and his collaborators gave rise to a great interest in quantum groups and Hopf algebras. Since then several other versions of (q-) deformed Lie algebras have appeared, especially in physical contexts such as string theory ...

AdS/CFT Course Notes - Johns Hopkins University

... A natural question: what if we have a theory that does not change when we zoom out? This would be a scale invariant theory. In the case of high energy physics, where we have Poincaré symmetry, scale invariant theories are basically always conformally invariant QFTs,3 which are called Conformal Fiel ...

... A natural question: what if we have a theory that does not change when we zoom out? This would be a scale invariant theory. In the case of high energy physics, where we have Poincaré symmetry, scale invariant theories are basically always conformally invariant QFTs,3 which are called Conformal Fiel ...

Free Field Approach to 2-Dimensional Conformal Field Theories

... finite dimensional algebra realization, but present instead a completely algebraic approach. We include a discussion of the "twisted Verma modules" of Feigin and Frenkel, 50>which are in some respects the closest finite dimensional analogues, since their corresponding resolutions turn out to be two- ...

... finite dimensional algebra realization, but present instead a completely algebraic approach. We include a discussion of the "twisted Verma modules" of Feigin and Frenkel, 50>which are in some respects the closest finite dimensional analogues, since their corresponding resolutions turn out to be two- ...

Endomorphism Bialgebras of Diagrams and of Non

... construct explicit examples of such and check all the necessary properties. This gets even more complicated if we have to verify that something like a comodule algebra over a bialgebra is given. Bialgebras and comodule algebras, however, arise in a very natural way in non-commutative geometry and in ...

... construct explicit examples of such and check all the necessary properties. This gets even more complicated if we have to verify that something like a comodule algebra over a bialgebra is given. Bialgebras and comodule algebras, however, arise in a very natural way in non-commutative geometry and in ...

Lecture notes: Group theory and its applications in physics

... complicated (system) of differential equations, which in exact form only in few exceptional cases (of integrable systems) is possible. On the other hand, it often happens that given an arbitrary solution q(t) one can construct a family of solutions by application of certain transformation to it: q(t ...

... complicated (system) of differential equations, which in exact form only in few exceptional cases (of integrable systems) is possible. On the other hand, it often happens that given an arbitrary solution q(t) one can construct a family of solutions by application of certain transformation to it: q(t ...

Twenty years of the Weyl anomaly

... many a recent convert, he went on to become their most ardent advocatet. This was also the beginning of a very fruitful collaboration between the two of us. The significance of my paper with Deser and Isham was that, with the exception of the OR term in (la), none of the above anomalies could be rem ...

... many a recent convert, he went on to become their most ardent advocatet. This was also the beginning of a very fruitful collaboration between the two of us. The significance of my paper with Deser and Isham was that, with the exception of the OR term in (la), none of the above anomalies could be rem ...

A Numerical Approach to Virasoro Blocks and the Information

... field theory. This means that to make progress, it will be crucial to be able to directly compare the approximate correlation functions of bulk EFT and the exact correlators of the CFT. AdS3 /CFT2 may provide the best opportunity for such comparisons. Many features of quantum gravity in AdS3 can be ...

... field theory. This means that to make progress, it will be crucial to be able to directly compare the approximate correlation functions of bulk EFT and the exact correlators of the CFT. AdS3 /CFT2 may provide the best opportunity for such comparisons. Many features of quantum gravity in AdS3 can be ...

Indecomposable Representations of the Square

... nonlinear Lie algebras and their applications in quantum systems.[1,2] In a previous paper,[3] we studied boson realizations of square-root Lie algebras of vector and quadratic types by means of Schwinger’s coupled boson representation of angular momentum theory. In this paper we shall study indecom ...

... nonlinear Lie algebras and their applications in quantum systems.[1,2] In a previous paper,[3] we studied boson realizations of square-root Lie algebras of vector and quadratic types by means of Schwinger’s coupled boson representation of angular momentum theory. In this paper we shall study indecom ...

A Group-Theoretical Approach to the Periodic Table of

... and the set {C1, X3} is a set of commuting operators. Note that, in the theory of angular momentum, the latter set corresponds to the set {J2, Jz} of the square J2 of a generalized angular momentum and its component Jz around an arbitrary axis. Going back to the general case of a semi-simple Lie alg ...

... and the set {C1, X3} is a set of commuting operators. Note that, in the theory of angular momentum, the latter set corresponds to the set {J2, Jz} of the square J2 of a generalized angular momentum and its component Jz around an arbitrary axis. Going back to the general case of a semi-simple Lie alg ...

A group-theoretical approach to the periodic table

... and the set {C1, X3} is a set of commuting operators. Note that, in the theory of angular momentum, the latter set corresponds to the set {J 2, Jz} of the square J2 of a generalized angular momentum and its component J z around an arbitrary axis. Going back to the general case of a semi-simple Lie a ...

... and the set {C1, X3} is a set of commuting operators. Note that, in the theory of angular momentum, the latter set corresponds to the set {J 2, Jz} of the square J2 of a generalized angular momentum and its component J z around an arbitrary axis. Going back to the general case of a semi-simple Lie a ...

QUANTUM GROUPS AND DIFFERENTIAL FORMS Contents 1

... skew-commute and then deform it to Ω(Aq ). These considerations are motivated by the generalised homological algebra of N -complexes [8]. Throughout this paper, we assume that N ≥ 2 and k is any field. 1.1. The commutative setting. Let V be the vector space over k with basis S = {x1 , . . . , xn }. ...

... skew-commute and then deform it to Ω(Aq ). These considerations are motivated by the generalised homological algebra of N -complexes [8]. Throughout this paper, we assume that N ≥ 2 and k is any field. 1.1. The commutative setting. Let V be the vector space over k with basis S = {x1 , . . . , xn }. ...

No. 18 - Department of Mathematics

... features of classical integrability, higher charges and Lax pairs, using as a toy model the theory of the principal chiral field (14). Starting from section 4, we enter the core of the topic of this review, i.e. the quantum group structure of the AdS/CFT S-matrix, based on the centrally-extended psl ...

... features of classical integrability, higher charges and Lax pairs, using as a toy model the theory of the principal chiral field (14). Starting from section 4, we enter the core of the topic of this review, i.e. the quantum group structure of the AdS/CFT S-matrix, based on the centrally-extended psl ...

Spontaneously Broken Symmetries

... and crucial eects in elementary particle physics and condensed matter physics are attributed to it [GHK]. Since this phenomenon was mainly studied within the context of quantum eld theory it became considered as typical for innite quantum systems. We shall study it in this paper in the context of ...

... and crucial eects in elementary particle physics and condensed matter physics are attributed to it [GHK]. Since this phenomenon was mainly studied within the context of quantum eld theory it became considered as typical for innite quantum systems. We shall study it in this paper in the context of ...

Multivariable Hypergeometric Functions Eric M. Opdam

... This projection is a ﬁbration with ﬁber π −1 (z) = Yz . We deﬁne a vector bundle H1twist (Y /X) over X whose ﬁber at z is the twisted homology group H1twist (Yz ). An element Cz0 ∈ H1twist (Yz0 ) naturally deﬁnes a twisted cycle in every ﬁber H1twist (Yz ) if z is suﬃciently close to z0 . Such local ...

... This projection is a ﬁbration with ﬁber π −1 (z) = Yz . We deﬁne a vector bundle H1twist (Y /X) over X whose ﬁber at z is the twisted homology group H1twist (Yz ). An element Cz0 ∈ H1twist (Yz0 ) naturally deﬁnes a twisted cycle in every ﬁber H1twist (Yz ) if z is suﬃciently close to z0 . Such local ...