Dirac Operators on Noncommutative Spacetimes ?

... of the classical Dirac operator, which at first seem equally well motivated and are not obviously equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac opera ...

... of the classical Dirac operator, which at first seem equally well motivated and are not obviously equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac opera ...

On the Classical and Quantum Momentum Map

... for the study of the so-called symplectic reduction of certain manifolds [40]. This method is a synthesis of different techniques of reduction of the phase space (generally a symplectic manifold) associated to a dynamical system, in which the symmetries are divided out. In particular, the Marsden-We ...

... for the study of the so-called symplectic reduction of certain manifolds [40]. This method is a synthesis of different techniques of reduction of the phase space (generally a symplectic manifold) associated to a dynamical system, in which the symmetries are divided out. In particular, the Marsden-We ...

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 ...

Towards the mathematics of quantum field theory

... between two spaces, that represents the motion of a physical object in a configuration space C, with parameter space M . The notion of space must be taken here in a widely generalized sense, because even electrons have a mathematical formalization as functions between spaces of a non-classical kind, ...

... between two spaces, that represents the motion of a physical object in a configuration space C, with parameter space M . The notion of space must be taken here in a widely generalized sense, because even electrons have a mathematical formalization as functions between spaces of a non-classical kind, ...

Algebraic Topology Foundations of Supersymmetry and Symmetry

... global-group, and/or group-like symmetries) with partial symmetries of paracrystals and glassy solids on the one hand, and also with non-commutative harmonic analysis [151] on the other hand, we propose that several extended quantum symmetries can be represented algebraically in terms of certain str ...

... global-group, and/or group-like symmetries) with partial symmetries of paracrystals and glassy solids on the one hand, and also with non-commutative harmonic analysis [151] on the other hand, we propose that several extended quantum symmetries can be represented algebraically in terms of certain str ...

Spin Squeezing, Entanglement and Quantum Metrology

... The interpretation of this representation on generalized Bloch spheres differs from the single spin j = 1/2 Bloch sphere shown in Fig. 2.1. In the latter case the dimension of the Hilbert space is two-dimensional and the quantum state representation on the surface of a sphere is exact. However for c ...

... The interpretation of this representation on generalized Bloch spheres differs from the single spin j = 1/2 Bloch sphere shown in Fig. 2.1. In the latter case the dimension of the Hilbert space is two-dimensional and the quantum state representation on the surface of a sphere is exact. However for c ...

Factorization Algebras in Quantum Field Theory Volume 1 (8 May

... this is precisely what we have described. As we explain in Section 4, this relationship continues and so our quantization theorem produces many new examples of algebras over the operad En of little n-discs. An important point to take away from this discussion is that associative algebras appear in q ...

... this is precisely what we have described. As we explain in Section 4, this relationship continues and so our quantization theorem produces many new examples of algebras over the operad En of little n-discs. An important point to take away from this discussion is that associative algebras appear in q ...

Boundary conditions for integrable quantum systems

... boundary conditions. As regards the systems on the finite interval with independent boundary conditions on each end, only a few cases solved either by the coordinate Bethe ansatz or directly are described in the literature. These are the Bose (Gaudin 1971, 1983) and Fermi gases (Woynarovich 1985), t ...

... boundary conditions. As regards the systems on the finite interval with independent boundary conditions on each end, only a few cases solved either by the coordinate Bethe ansatz or directly are described in the literature. These are the Bose (Gaudin 1971, 1983) and Fermi gases (Woynarovich 1985), t ...

ENGR-36_Lec - Chabot College

... Any Student can Work at his/her own Time & Location in place of the lab AS LONG AS the LPS are Submitted to Mastering Engineering ON TIME If a student can not make the Lab Session, I suggest forming an ENGR36 study Group outside of class times Engineering-36: Vector Mechanics - Statics ...

... Any Student can Work at his/her own Time & Location in place of the lab AS LONG AS the LPS are Submitted to Mastering Engineering ON TIME If a student can not make the Lab Session, I suggest forming an ENGR36 study Group outside of class times Engineering-36: Vector Mechanics - Statics ...

Lie algebra decompositions with applications to quantum dynamics

... concatenation of these control functions give the full control that drives X to the desired target state Xf . It is clear that some decompositions may be more convenient than others, depending on the particular situation at hand. Hence, it is important to have several ways to decompose the Lie group ...

... concatenation of these control functions give the full control that drives X to the desired target state Xf . It is clear that some decompositions may be more convenient than others, depending on the particular situation at hand. Hence, it is important to have several ways to decompose the Lie group ...

An Optimal Whitening Approach to Linear Multiuser Detection

... orthogonal multiuser (OMU) receiver was proposed as a compromise between the MF and the decorrelator [2], [3]. Like the MF and the decorrelator, this receiver requires knowledge of the signature vectors only and is, therefore, designed to operate in environments in which the channel parameters are u ...

... orthogonal multiuser (OMU) receiver was proposed as a compromise between the MF and the decorrelator [2], [3]. Like the MF and the decorrelator, this receiver requires knowledge of the signature vectors only and is, therefore, designed to operate in environments in which the channel parameters are u ...

On quantum detection and the square

... Therefore, let be a collection of normalized in an -dimensional complex Hilbert space . Convectors by choosisng approcretely, we may always identify with priate coordinates. In general, these vectors are nonorthogonal . The vectors are and span an -dimensional subspace ...

... Therefore, let be a collection of normalized in an -dimensional complex Hilbert space . Convectors by choosisng approcretely, we may always identify with priate coordinates. In general, these vectors are nonorthogonal . The vectors are and span an -dimensional subspace ...

Document

... the Wineland sense. But this does not mean that all states with no Wineland squeezing are of fully separable form In particular, there can be entangled states with ...

... the Wineland sense. But this does not mean that all states with no Wineland squeezing are of fully separable form In particular, there can be entangled states with ...

Chapter 8: Vectors and Parametric Equations

... We can find the magnitude and direction of the resultant by drawing vectors to represent the forces on the stretcher. However, drawings can be inaccurate and quite confusing for more complex systems of vectors. In cases where more accuracy is necessary or where the system is more complicated, we can ...

... We can find the magnitude and direction of the resultant by drawing vectors to represent the forces on the stretcher. However, drawings can be inaccurate and quite confusing for more complex systems of vectors. In cases where more accuracy is necessary or where the system is more complicated, we can ...

Fractional Spin Liquid Hierarchy for Spin S

... mentioned examples such as the quantum Hall effect or topological insulators generally promise a rather accessible ...

... mentioned examples such as the quantum Hall effect or topological insulators generally promise a rather accessible ...