Contents
... invariance – and represent the interaction under study. If the symmetry group is non-commutative, it is referred to as nonAbelian, like in the Yang–Mills theory that is briefly addressed in the appendix. When the theory is quantized, the quanta of the gauge fields are called gauge bosons. Quantum e ...
... invariance – and represent the interaction under study. If the symmetry group is non-commutative, it is referred to as nonAbelian, like in the Yang–Mills theory that is briefly addressed in the appendix. When the theory is quantized, the quanta of the gauge fields are called gauge bosons. Quantum e ...
Particle Physics Part III Major Option 2008
... • at low ET cross-section is dominated by low x partons i.e. gluon-gluon scattering • at high ET cross-section is dominated by high x partons i.e. quark-antiquark scattering ...
... • at low ET cross-section is dominated by low x partons i.e. gluon-gluon scattering • at high ET cross-section is dominated by high x partons i.e. quark-antiquark scattering ...
Lectures on the Geometry of Quantization
... Ĥ. As soon as we wish to “quantize” a more complicated energy function, such as (1 + q 2 )p2 , we run in to the problem that the operators q̂ and p̂ do not commute with one another, so that we are forced to choose between (1 + q̂ 2 )p̂2 and p̂2 (1 + q̂ 2 ), among a number of other possibilities. Th ...
... Ĥ. As soon as we wish to “quantize” a more complicated energy function, such as (1 + q 2 )p2 , we run in to the problem that the operators q̂ and p̂ do not commute with one another, so that we are forced to choose between (1 + q̂ 2 )p̂2 and p̂2 (1 + q̂ 2 ), among a number of other possibilities. Th ...
Beyond the Standard Model
... The first version of these notes was written up for lectures at the 1995 AIO-school (a school for PhD students) on theoretical particle physics. Later they were adapted for lectures at the Radboud University in Nijmegen, aimed at undergraduate students in their fourth year. This means that no detail ...
... The first version of these notes was written up for lectures at the 1995 AIO-school (a school for PhD students) on theoretical particle physics. Later they were adapted for lectures at the Radboud University in Nijmegen, aimed at undergraduate students in their fourth year. This means that no detail ...
Introduction to Group Field Theory
... Requirement: the GFT theory space should be stable enough under renormalization / coarse-graining. ...
... Requirement: the GFT theory space should be stable enough under renormalization / coarse-graining. ...
A Glimpse into Symplectic Geometry
... • Symplectic structures first arose in the Hamiltonian formulation of the theory of classical mechanics and this tight interconnection with physics has persisted ever since. A longstanding mystery in mathematics that is especially striking now is the extraordinary power of ideas from physics, specia ...
... • Symplectic structures first arose in the Hamiltonian formulation of the theory of classical mechanics and this tight interconnection with physics has persisted ever since. A longstanding mystery in mathematics that is especially striking now is the extraordinary power of ideas from physics, specia ...
Lattice quantum field theory
... U(a, b, T = tN − t0 ) = a, tN e−iHT b, t0 . In the next step, insert at intermediate times a sum, or integral in cases of a continuous ...
... U(a, b, T = tN − t0 ) = a, tN e−iHT b, t0 . In the next step, insert at intermediate times a sum, or integral in cases of a continuous ...
Haag`s Theorem in Renormalisable Quantum Field Theories
... • First, all approaches to construct quantum field models in a way seen as mathematically sound and rigorous employ methods from operator theory and stochastic analysis, the latter only in the Euclidean case. This is certainly natural given the corresponding heuristically very successful notions use ...
... • First, all approaches to construct quantum field models in a way seen as mathematically sound and rigorous employ methods from operator theory and stochastic analysis, the latter only in the Euclidean case. This is certainly natural given the corresponding heuristically very successful notions use ...
here
... Properties of Majorana Fermions Non-abelian statistics A system of 2N well separated Majoranas has a 2N degenerate ground state. Think of N independent of 1-D Kitaev chains Exchanging or “braiding” connects two different ground states What is nonabelian about them? “if one performs sequenti ...
... Properties of Majorana Fermions Non-abelian statistics A system of 2N well separated Majoranas has a 2N degenerate ground state. Think of N independent of 1-D Kitaev chains Exchanging or “braiding” connects two different ground states What is nonabelian about them? “if one performs sequenti ...
here
... Properties of Majorana Fermions Non-abelian statistics A system of 2N well separated Majoranas has a 2N degenerate ground state. Think of N independent of 1-D Kitaev chains Exchanging or “braiding” connects two different ground states What is nonabelian about them? “if one performs sequenti ...
... Properties of Majorana Fermions Non-abelian statistics A system of 2N well separated Majoranas has a 2N degenerate ground state. Think of N independent of 1-D Kitaev chains Exchanging or “braiding” connects two different ground states What is nonabelian about them? “if one performs sequenti ...
Effective Field Theory
... taking into account the corrections induced by the neglected energy scales as small perturbations. Effective field theories are the appropriate theoretical tool to describe low-energy physics, where low is defined with respect to some energy scale Λ. They only take explicitly into account the releva ...
... taking into account the corrections induced by the neglected energy scales as small perturbations. Effective field theories are the appropriate theoretical tool to describe low-energy physics, where low is defined with respect to some energy scale Λ. They only take explicitly into account the releva ...
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 ...
Vladimirov A.A., Diakonov D. Diffeomorphism
... the diffeomorphism invariance is the invariance of the action under the arbitrary continuous vertex displacement. It means that the lattice action should depend only on the topology, i.e., on the neighborhood structure of the lattice. We call the lattice the ®number space¯. 1.1. General Construction ...
... the diffeomorphism invariance is the invariance of the action under the arbitrary continuous vertex displacement. It means that the lattice action should depend only on the topology, i.e., on the neighborhood structure of the lattice. We call the lattice the ®number space¯. 1.1. General Construction ...
Non-linear field theory with supersymmetry
... as well as in astrophysics and cosmology [10, 11]. As it is also believed to provide a more accurate description of hydrodynamical phenomena, much work has been invested in its development [51, 52]. Recently, an interesting extension of the theory to include non-abelian charges and currents has been ...
... as well as in astrophysics and cosmology [10, 11]. As it is also believed to provide a more accurate description of hydrodynamical phenomena, much work has been invested in its development [51, 52]. Recently, an interesting extension of the theory to include non-abelian charges and currents has been ...
Functorial Field Theories and Factorization Algebras
... of reverse engineering: in each of these cases, we need to construct a suitable action function such that the associated Euler-Lagrange equation characterizing the critical points of S is the differential equation we start with. ...
... of reverse engineering: in each of these cases, we need to construct a suitable action function such that the associated Euler-Lagrange equation characterizing the critical points of S is the differential equation we start with. ...
A unification of photons, electrons, and gravitons under qbit
... • The symmetry breaking states can only give rise to bosonic collective excitations described by bosonic field ∼ order parameters. But no gauge bosons and fermions. How to get gauge bosons and fermions from qbit models? • The symmetry breaking states are “trivial” unentangled states: |symm. breaking ...
... • The symmetry breaking states can only give rise to bosonic collective excitations described by bosonic field ∼ order parameters. But no gauge bosons and fermions. How to get gauge bosons and fermions from qbit models? • The symmetry breaking states are “trivial” unentangled states: |symm. breaking ...
A Group-Theoretical Approach to the Periodic Table of
... element of G there corresponds a matrix of GL(m, C) such that the composition rules for G and GL(m, C) are conserved by this correspondence. Among the various representations of a group, the unitary irreducible representations play a central role. From the mathematical viewpoint, a unitary irreducib ...
... element of G there corresponds a matrix of GL(m, C) such that the composition rules for G and GL(m, C) are conserved by this correspondence. Among the various representations of a group, the unitary irreducible representations play a central role. From the mathematical viewpoint, a unitary irreducib ...
The AdS/CFT Correspondence arXiv:1501.00007
... divergences become uncontrollably worse at each order. This indicates that some new physics has to kick in to modify general relativity in the UV (meaning short distances or high energy scales). An ingenious way to tame these divergences is to consider strings as the fundamental degrees of freedom ( ...
... divergences become uncontrollably worse at each order. This indicates that some new physics has to kick in to modify general relativity in the UV (meaning short distances or high energy scales). An ingenious way to tame these divergences is to consider strings as the fundamental degrees of freedom ( ...
Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence Jan Plefka
... candidate for a unified quantum theory of gravity and all the other forces of nature. In this interpretation, gauge fields arise as the low energy excitations of fundamental open strings and are therefore derived, non-fundamental objects, just as the theory of gravity itself. Ironically though, adva ...
... candidate for a unified quantum theory of gravity and all the other forces of nature. In this interpretation, gauge fields arise as the low energy excitations of fundamental open strings and are therefore derived, non-fundamental objects, just as the theory of gravity itself. Ironically though, adva ...
A group-theoretical approach to the periodic table
... element of G there corresponds a matrix of GL(m, C) such that the composition rules for G and GL(m, C) are conserved by this correspondence. Among the various representations of a group, the unitary irreducible representations play a central role. From the mathematical viewpoint, a unitary irreducib ...
... element of G there corresponds a matrix of GL(m, C) such that the composition rules for G and GL(m, C) are conserved by this correspondence. Among the various representations of a group, the unitary irreducible representations play a central role. From the mathematical viewpoint, a unitary irreducib ...
Renormalisation of Noncommutative Quantum Field Theory
... classical action functionals on noncommutative spaces. The first example of this type was Yang-Mills theory on the noncommutative torus. Another example is the noncommutative geometrical description of the Standard Model recalled briefly in Section 1.1. 3.1 Field theory on the noncommutative torus T ...
... classical action functionals on noncommutative spaces. The first example of this type was Yang-Mills theory on the noncommutative torus. Another example is the noncommutative geometrical description of the Standard Model recalled briefly in Section 1.1. 3.1 Field theory on the noncommutative torus T ...
Effective Field Theories in Cosmology - SUrface
... either additional degrees of freedom besides the graviton or violations of Lorentz symmetry. We also review the mechanism which leads to the generation of primordial fluctuations during inflation. In chapter 3, we study theories of gravitation which admit violations of Lorentz symmetry. By extending ...
... either additional degrees of freedom besides the graviton or violations of Lorentz symmetry. We also review the mechanism which leads to the generation of primordial fluctuations during inflation. In chapter 3, we study theories of gravitation which admit violations of Lorentz symmetry. By extending ...
See the slides
... The general path integral is not rigorously defined for curved space of fields. Idea: postulate the value of the path integral looking as infinite-dimensional δ-function, it localizes to the finite-dimensional space of generalized instantons. ...
... The general path integral is not rigorously defined for curved space of fields. Idea: postulate the value of the path integral looking as infinite-dimensional δ-function, it localizes to the finite-dimensional space of generalized instantons. ...