119158624
Block Diagonalization using SRG Flow Equations
Here s is a flow parameter and the flow operator Gs specifies the type of SRG [4]. Decoupling between low-energy and high-energy matrix elements is naturally achieved in a momentum basis by choosing a momentum-diagonal flow operator such as the kinetic energy Trel or the diagonal of Hs; either drives the Hamiltonian toward banddiagonal form. This decoupling leads to dramatically improved variational convergence in few-body nuclear systems compared to unevolved phenomenological or chiral EFT potentials [5, 6]. Renormalization Group (RG) methods that evolve NN interactions with a sharp or smooth cutoff in relative momentum, known generically as Vlow k, rely on the invariance of the two-nucleon T matrix [7, 8]. These approaches achieve a block-diagonal form characterized by a cutoff Λ (see left plots in Figs. 1 and 2). As usually implemented they set the high-momentum matrix elements to zero but this is not required. Block-diagonal decoupling of the sharp Vlow k form can
119292607
Operator evolution via the similarity renormalization group: The deuteron
Similarity renormalization group (SRG)flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate-state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less-correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this article on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator. DOI: 10.1103/PhysRevC.82.054001
119312110
Shape space methods for quantum cosmological triangleland
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so by importing techniques to the triangle model from the corresponding 4 particles in 1-d model, using the fact that both have 2-spheres for shape spaces, though the latter has a trivial realization whilst the former has a more involved Hopf (or Dragt) type realization. I furthermore interpret the ensuing Dragt-type coordinates as shape quantities: a measure of anisoscelesness, the ellipticity of the base and apex’s moments of inertia, and a quantity proportional to the area of the triangle. I promote these quantities at the quantum level to operators whose expectation and spread are then useful in understanding the quantum states of the system. Additionally, I tessellate the 2-sphere by its physical interpretation as the shape space of triangles, and then use this as a back-cloth from which to read off the interpretation of dynamical trajectories, potentials and wavefunctions. I include applications to timeless approaches to the problem of time and to the role of uniform states in quantum cosmological modelling.
121981552
Observation and study of centrally produced pion clusters in 28. 5-GeV/c p-p interactions
A double-arm spectrometer is used to identify a pion cluster produced in central p-p collisions at 28.5 GeV/c. Cluster properties studied are angular momentum, quantum statistics, multiplicity, and effective mass. There is some speculation on the production mechanism. (AIP)
14145110
Relational motivation for conformal operator ordering in quantum cosmology
Operator ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. This arises particularly naturally and simply from relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein–Sharp–Wheeler-type actions for general relativity), for which all that is required is for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implement philosophical principles relevant to whole-universe modelling, so that the motivation for conformal operator ordering in quantum cosmology is thereby substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in various contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler–Lagrange or Arnowitt–Deser–Misner-type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the emergent time permits relating how this simplifies equations of motion with how affine parametrization simplifies geodesics.
119270516
An interpretation of variational principles for gauge theories: a cyclic coordinate alternative to ADM split
I show that there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. (This is also known as variation with natural boundary conditions.) Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new flux, instant and grid variables whose corresponding velocities are, respectively, the above-mentioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations as regards variational principles for the conformal form of general relativity's initial value problem.
122516925
Isobar production and elastic scattering in p p interactions from 6-GeV/c to 30-GeV/c