Deconfined Quantum Critical Points
... condensed matter theory. A central concept in this theory is that of the ”order parameter”; its nonzero expectation value characterizes a broken symmetry of the Hamiltonian in an ordered phase and it goes to zero when the symmetry is restored in the disordered phase. According to the accepted paradi ...
... condensed matter theory. A central concept in this theory is that of the ”order parameter”; its nonzero expectation value characterizes a broken symmetry of the Hamiltonian in an ordered phase and it goes to zero when the symmetry is restored in the disordered phase. According to the accepted paradi ...
Introduction to Integrable Models
... the so-called coordinate Bethe ansatz. It has the virtue of being very intuitive and will give us a good understanding of the physics of the spin chain. Its drawback is that it cannot be generalized very much. We will therefore graduate to the more abstract, but much more powerful algebraic Bethe an ...
... the so-called coordinate Bethe ansatz. It has the virtue of being very intuitive and will give us a good understanding of the physics of the spin chain. Its drawback is that it cannot be generalized very much. We will therefore graduate to the more abstract, but much more powerful algebraic Bethe an ...
Quantum field theory and the Jones polynomial
... polynomial corresponds to the case that G is SU(N), and the R~ are all the defining N dimensional representation of SU(N). The two variables are N and k, analytically continued to complex values. The Kauffman polynomial similarly arises for G -- SO (N) and R the N dimensional representation. (2) As ...
... polynomial corresponds to the case that G is SU(N), and the R~ are all the defining N dimensional representation of SU(N). The two variables are N and k, analytically continued to complex values. The Kauffman polynomial similarly arises for G -- SO (N) and R the N dimensional representation. (2) As ...
Nonperturbative quantum geometries
... (i) All states of the form (1.13) are annihilated by the hamiltonian constraint (1.14), as long as the curves "/~ are differentiable, and without intersection. (ii) When an intersection point occurs, certain additional conditions must be satisfied for a state to be annihilated by the hamiltonian con ...
... (i) All states of the form (1.13) are annihilated by the hamiltonian constraint (1.14), as long as the curves "/~ are differentiable, and without intersection. (ii) When an intersection point occurs, certain additional conditions must be satisfied for a state to be annihilated by the hamiltonian con ...
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Effective Field Theories for Topological states of Matter
... fermions, which are classified according their dimension and symmetry properties[3, 4]. The classes can be trivial or non-trivial. The latter are characterized by a non-trivial value of a topological index that can either take integer values, a Z index, or the values ±1 which is a Z2 index. If we ch ...
... fermions, which are classified according their dimension and symmetry properties[3, 4]. The classes can be trivial or non-trivial. The latter are characterized by a non-trivial value of a topological index that can either take integer values, a Z index, or the values ±1 which is a Z2 index. If we ch ...
doc - StealthSkater
... 3. One can, of course, argue it is not clear whether stringy gravitons represent hadron-like objects responsible for strong gravitation below relevant p-adic length scale rather than genuine gravitons. For instance, the identification of elementary particles in terms of CP2 type extremals forces to ...
... 3. One can, of course, argue it is not clear whether stringy gravitons represent hadron-like objects responsible for strong gravitation below relevant p-adic length scale rather than genuine gravitons. For instance, the identification of elementary particles in terms of CP2 type extremals forces to ...
Quantum field theory for matter under extreme conditions
... with the Lorentz transformations – rotations and boosts – and the four associated with translations. Quantum mechanics describes the time evolution of a system with interactions, and that evolution is generated by the Hamiltonian. However, if the theory is formulated with an interacting Hamiltonian ...
... with the Lorentz transformations – rotations and boosts – and the four associated with translations. Quantum mechanics describes the time evolution of a system with interactions, and that evolution is generated by the Hamiltonian. However, if the theory is formulated with an interacting Hamiltonian ...
Band-gap structure and chiral discrete solitons in optical lattices with
... interaction strengths gn/J and different magnetic fluxes φ. For noninteracting systems, the analytical band-gap structures can be obtained by exactly diagonalizing the Hamiltonian matrix (7). When the magnetic flux φ increases, the lowest band gradually changes from a singlewell shape to a three-wel ...
... interaction strengths gn/J and different magnetic fluxes φ. For noninteracting systems, the analytical band-gap structures can be obtained by exactly diagonalizing the Hamiltonian matrix (7). When the magnetic flux φ increases, the lowest band gradually changes from a singlewell shape to a three-wel ...
Phys. Rev. Lett. 104, 255303
... momenta k equal to reciprocal lattice vectors [26]. (Note that the natural gauge for time-of-flight measurements depends on the experimental procedure. We use the Landau gauge appropriate to current experiments with artificial gauge potentials [11,12].) The peak for k ¼ nX þ P ‘Y has intensity j A ...
... momenta k equal to reciprocal lattice vectors [26]. (Note that the natural gauge for time-of-flight measurements depends on the experimental procedure. We use the Landau gauge appropriate to current experiments with artificial gauge potentials [11,12].) The peak for k ¼ nX þ P ‘Y has intensity j A ...
The Family Problem: Extension of Standard Model with a
... similarity principle – our struggle of eighty years to describe the point-like particles such as the electron. The “minimum Higgs hypothesis” is the other mysterious conjecture – because we are looking for Higgs particles for forty years, but so far none has been found. So, by “induction”, we tr ...
... similarity principle – our struggle of eighty years to describe the point-like particles such as the electron. The “minimum Higgs hypothesis” is the other mysterious conjecture – because we are looking for Higgs particles for forty years, but so far none has been found. So, by “induction”, we tr ...
Gauge fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions ""perpendicular"" to them. Hence there is an enormous amount of freedom involved in taking a ""cross section"" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.